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<!doctype html> <html lang=en> <head> <meta charset=utf-8> <title>Quantum field theory - Ciro Santilli</title> <meta name="viewport" content="width=device-width, initial-scale=1"> <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.10.1/css/all.min.css" integrity="sha512-9my9Mb2+0YO+I4PUCSwUYO7sEK21Y0STBAiFEYoWtd2VzLEZZ4QARDrZ30hdM1GlioHJ8o8cWQiy8IAb1hy/Hg==" crossorigin="anonymous" referrerpolicy="no-referrer"> <style>@import "_obb/dist/ourbigbook.css"; </style> <link rel="stylesheet" type="text/css" href="_raw/main.css"> <link rel="shortcut icon" type="image/x-icon" href="https://raw.githubusercontent.com/cirosantilli/media/master/ID_photo_of_Ciro_Santilli_taken_in_2013_square_398.jpg"> </head> <body> <header> <div class="brand-group"> <a href="." class="brand"><img src="https://raw.githubusercontent.com/cirosantilli/media/master/ID_photo_of_Ciro_Santilli_taken_in_2013_right_eye_200_100.jpg" loading="lazy" alt="ID photo of Ciro Santilli taken in 2013 right eye">Ciro Santilli</a> <a href="https://ourbigbook.com/cirosantilli"><img src="https://raw.githubusercontent.com/cirosantilli/media/master/ourbigbook-logo-v1.svg" loading="lazy" alt="OurBigBook logo">OurBigBook.com</a> <a class="font-awesome-container" href="https://stackoverflow.com/users/895245"><i class="fab fa-stack-overflow fa-fw icon"></i></a> <a class="font-awesome-container" href="https://github.com/cirosantilli"><i class="fab fa-github fa-fw icon"></i></a> <a class="font-awesome-container" href="https://www.linkedin.com/in/cirosantilli"><i class="fab fa-linkedin fa-fw icon"></i></a> <a class="font-awesome-container" href="https://www.youtube.com/c/CiroSantilli"><i class="fab fa-youtube fa-fw icon"></i></a> <a class="font-awesome-container" href="https://twitter.com/cirosantilli"><i class="fab fa-twitter fa-fw icon"></i></a> <a class="font-awesome-container" href="https://www.zhihu.com/people/cirosantilli/activities"><i class="fab fa-zhihu fa-fw icon"></i></a> <a class="font-awesome-container" href="https://www.weibo.com/p/1005055601627311"><i class="fab fa-weibo fa-fw icon"></i></a> <a href="sponsor"><span class="icon">$£</span> Sponsor</a> <a href="https://github.com/cirosantilli/china-dictatorship"><span class="icon">中国</span>独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件邓家贵、低端人口、西藏骚乱</a> </div> </header> <main class="ourbigbook"> <div class="h top" id="quantum-field-theory"><div class="notnav"><h1><a href="quantum-field-theory-split">Quantum field theory <span class="meta">(QFT)</span></a></h1></div><nav class="h-nav h-nav-toplevel"><div class="nav ancestors"><a href="#_ancestors"> ...</a><a href="science"> Science</a><a href="science#natural-science"> Natural science</a><a href="physics"> Physics</a><a href="particle-physics"> Particle physics</a><a href="quantum-mechanics"> Quantum mechanics</a><a href="relativistic-quantum-mechanics"> Relativistic quantum mechanics</a></div><div class="nav"><a href="#_toc" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="ciro-santilli-s-psychology-and-physiology#ciro-santilli-s-fetishes">Ciro Santilli's fetishes</a></span><a class="split" href="quantum-field-theory-split"></a><span class="metrics"><span class="wcntr"> Words: 6k</span><span class="dcnt"> Articles: 114</span></span></div></nav></div><div class="p" id="_3">Theoretical framework on which quantum field theories are based, theories based on framework include:<div class="list"><ul id="_4"><li id="_5"><a href="#quantum-electrodynamics">quantum electrodynamics</a></li><li id="_6"><a href="#quantum-chromodynamics">quantum chromodynamics</a></li></ul></div>so basically the entire <a href="standard-model">Standard Model</a></div><div class="p" id="_7">The basic idea is that there is a field for each particle particle type.</div><div class="p" id="_8">E.g. in QED, one for the <a href="standard-model#electron">electron</a> and one for the <a href="photon">photon</a>: <a href="https://physics.stackexchange.com/questions/166709/are-electron-fields-and-photon-fields-part-of-the-same-field-in-qed">physics.stackexchange.com/questions/166709/are-electron-fields-and-photon-fields-part-of-the-same-field-in-qed</a>.</div><div class="p" id="_9">And then those fields interact with some <a href="mechanics#lagrangian">Lagrangian</a>.</div><div class="p" id="_10">One way to look at QFT is to split it into two parts:<div class="list"><ul id="_11"><li id="_12">deriving the Lagrangians of the <a href="standard-model">Standard Model</a>: <a href="linguistics#s">S</a>. This is the easier part, since the lagrangians themselves can be understood with not very advanced mathematics, and derived beautifully from symmetry constraints</li><li id="_13">the qantization of fields. This is the hard part <a href="ciro-santilli">Ciro Santilli</a> is unable to understand, TODO <a href="#mathematical-formulation-of-quantum-field-theory">mathematical formulation of quantum field theory</a>.</li></ul></div>Then interwined with those two is the part "OK, how to solve the equations, if they are solvable at all", which is an open problem: <a href="#yang-mills-existence-and-mass-gap">Yang-Mills existence and mass gap</a>.</div><div class="p" id="_14">There appear to be two main equivalent formulations of quantum field theory:<div class="list"><ul id="_15"><li id="_16"><a href="#second-quantization">second quantization</a></li><li id="_17"><a href="#path-integral-formulation">path integral formulation</a></li></ul></div></div><div class="figure"><figure id="video-quantum-field-theory-visualized-by-scienceclic-english-2020" class="multiline"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/MmG2ah5Df4g" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-quantum-field-theory-visualized-by-scienceclic-english-2020"><span class="caption-prefix">Video 1. </span></a><div class="title">Quantum Field Theory visualized by <a href="physics#scienceclic">ScienceClic</a> English (2020)</div> <a href="https://www.youtube.com/watch?v=MmG2ah5Df4g">Source</a>. Gives one piece of possibly OK intuition: quantum theories kind of model all possible evolutions of the system at the same time, but with different probabilities. QFT is no different in that aspect.<div class="list"><ul id="_18"><li id="_19"><a href="https://youtu.be/MmG2ah5Df4g?t=209">youtu.be/MmG2ah5Df4g?t=209</a> describes how the <a href="relativistic-quantum-mechanics#spin-number-of-a-field">spin number of a field</a> is directly related to how much you have to rotate an element to reach the original position</li><li id="_20"><a href="https://youtu.be/MmG2ah5Df4g?t=480">youtu.be/MmG2ah5Df4g?t=480</a> explains which particles are modelled by which spin number</li></ul></div></figcaption></figure></div><div class="figure"><figure id="video-quantum-fields-the-real-building-blocks-of-the-universe-by-david-tong-2017" class="multiline"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/zNVQfWC_evg" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-quantum-fields-the-real-building-blocks-of-the-universe-by-david-tong-2017"><span class="caption-prefix">Video 2. </span></a><div class="title">Quantum Fields: The Real Building Blocks of the Universe by <a href="physicist#david-tong">David Tong</a> (2017)</div> <a href="https://youtu.be/zNVQfWC_evg">Source</a>. Boring, does not give anything except the usual blabla everyone knows from Googling:<div class="list"><ul id="_21"><li id="_22"><a href="https://youtu.be/zNVQfWC_evg?t=1335">youtu.be/zNVQfWC_evg?t=1335</a> shows <a href="https://www.youtube.com/watch?v=9TJe1Pr5c9Q">www.youtube.com/watch?v=9TJe1Pr5c9Q</a> from <a href="#quantum-field-theory-simulations">quantum field theory simulations</a></li><li id="_23"><a href="https://youtu.be/zNVQfWC_evg?t=1522">youtu.be/zNVQfWC_evg?t=1522</a> alludes to the <a href="algebra#birch-and-swinnerton-dyer-conjecture">Birch and Swinnerton-Dyer conjecture</a></li></ul></div></figcaption></figure></div><div class="figure"><figure id="video-quantum-field-theory-what-is-a-particle-by-physics-explained-2021"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/QPAxzr6ihu8" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-quantum-field-theory-what-is-a-particle-by-physics-explained-2021"><span class="caption-prefix">Video 3. </span></a><div class="title">Quantum Field Theory: What is a particle? by <a href="physics#physics-explained">Physics Explained</a> (2021)</div> <a href="https://www.youtube.com/watch?v=QPAxzr6ihu8">Source</a>. Gives some high level analogies between high level principles of <a href="quantum-mechanics#non-relativistic-quantum-mechanics">non-relativistic quantum mechanics</a> and <a href="relativity#special-relativity">special relativity</a> in to suggest that there is a minimum quanta of a relativistic quantum field.</figcaption></figure></div><div class="toc-container" id="_toc"><ul><li class="has-child toplevel"><div class="title-div"><div class="arrow"><div></div></div><span class="not-arrow"><a class="title toc" href="#_toc"> Table of contents</a><input class="search" placeholder="🔍 Search. Shortcut: / (slash)"></input><span class="hover-metadata"><span class="metrics"><span class="wcntr"> 6k</span><span class="dcnt"> 114</span></span></span></span></div><ul><li><div id="_toc/quantum-field"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field">Quantum field</a><span class="hover-metadata"><a class="split" href="quantum-field"></a><a href="#_toc" class="u"> Quantum field theory</a></span></span></div></li><li class="has-child"><div id="_toc/mathematical-formulation-of-quantum-field-theory"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#mathematical-formulation-of-quantum-field-theory">Mathematical formulation of quantum field theory</a><span class="hover-metadata"><a class="split" href="mathematical-formulation-of-quantum-field-theory"></a><a href="#_toc" class="u"> Quantum field theory</a><span class="metrics"><span class="wcntr"> 884</span><span class="dcnt"> 19</span></span></span></span></div><ul><li class="has-child"><div id="_toc/gauge-theory"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#gauge-theory">Gauge theory</a><span class="hover-metadata"><a class="split" href="gauge-theory"></a><a href="#_toc/mathematical-formulation-of-quantum-field-theory" class="u"> Mathematical formulation of quantum field theory</a><span class="metrics"><span class="wcntr"> 126</span><span class="dcnt"> 3</span></span></span></span></div><ul><li><div id="_toc/lattice-gauge-theory"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#lattice-gauge-theory">Lattice gauge theory</a><span class="hover-metadata"><a class="split" href="lattice-gauge-theory"></a><a href="#_toc/gauge-theory" class="u"> Gauge theory</a></span></span></div></li><li><div id="_toc/gauge-field"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#gauge-field">Gauge field</a><span class="hover-metadata"><a class="split" href="gauge-field"></a><a href="#_toc/gauge-theory" class="u"> Gauge theory</a><span class="metrics"><span class="wcntr"> 17</span></span></span></span></div></li><li><div id="_toc/gauge-symmetry"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#gauge-symmetry">Gauge symmetry</a><span class="hover-metadata"><a class="split" href="gauge-symmetry"></a><a href="#_toc/gauge-theory" class="u"> Gauge theory</a><span class="metrics"><span class="wcntr"> 61</span></span></span></span></div></li></ul><li><div id="_toc/fock-space"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#fock-space">Fock space</a><span class="hover-metadata"><a class="split" href="fock-space"></a><a href="#_toc/mathematical-formulation-of-quantum-field-theory" class="u"> Mathematical formulation of quantum field theory</a><span class="metrics"><span class="wcntr"> 14</span></span></span></span></div></li><li class="has-child"><div id="_toc/second-quantization"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#second-quantization">Second quantization</a><span class="hover-metadata"><a class="split" href="second-quantization"></a><a href="#_toc/mathematical-formulation-of-quantum-field-theory" class="u"> Mathematical formulation of quantum field theory</a><span class="metrics"><span class="wcntr"> 93</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/canonical-quantization"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#canonical-quantization">Canonical quantization</a><span class="hover-metadata"><a class="split" href="canonical-quantization"></a><a href="#_toc/second-quantization" class="u"> Second quantization</a><span class="metrics"><span class="wcntr"> 5</span></span></span></span></div></li></ul><li class="has-child"><div id="_toc/path-integral-formulation"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#path-integral-formulation">Path integral formulation</a><span class="hover-metadata"><a class="split" href="path-integral-formulation"></a><a href="#_toc/mathematical-formulation-of-quantum-field-theory" class="u"> Mathematical formulation of quantum field theory</a><span class="metrics"><span class="wcntr"> 131</span><span class="dcnt"> 3</span></span></span></span></div><ul><li><div id="_toc/quantum-particles-take-all-possible-paths"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-particles-take-all-possible-paths">Quantum particles take all possible paths</a><span class="hover-metadata"><a class="split" href="quantum-particles-take-all-possible-paths"></a><a href="#_toc/path-integral-formulation" class="u"> Path integral formulation</a><span class="metrics"><span class="wcntr"> 22</span></span></span></span></div></li><li><div id="_toc/propagator"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#propagator">Propagator</a><span class="hover-metadata"><a class="split" href="propagator"></a><a href="#_toc/path-integral-formulation" class="u"> Path integral formulation</a></span></span></div></li><li><div id="_toc/infinitely-many-slits-thought-experiment"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#infinitely-many-slits-thought-experiment">Infinitely many slits thought experiment</a><span class="hover-metadata"><a class="split" href="infinitely-many-slits-thought-experiment"></a><a href="#_toc/path-integral-formulation" class="u"> Path integral formulation</a><span class="metrics"><span class="wcntr"> 13</span></span></span></span></div></li></ul><li class="has-child"><div id="_toc/renormalization"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#renormalization">Renormalization</a><span class="hover-metadata"><a class="split" href="renormalization"></a><a href="#_toc/mathematical-formulation-of-quantum-field-theory" class="u"> Mathematical formulation of quantum field theory</a><span class="metrics"><span class="wcntr"> 316</span><span class="dcnt"> 7</span></span></span></span></div><ul><li><div id="_toc/mass-renormalization"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#mass-renormalization">Mass renormalization</a><span class="hover-metadata"><a class="split" href="mass-renormalization"></a><a href="#_toc/renormalization" class="u"> Renormalization</a></span></span></div></li><li><div id="_toc/renormalization-group"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#renormalization-group">Renormalization group</a><span class="hover-metadata"><a class="split" href="renormalization-group"></a><a href="#_toc/renormalization" class="u"> Renormalization</a></span></span></div></li><li><div id="_toc/cutoff-energy"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#cutoff-energy">Cutoff energy</a><span class="hover-metadata"><a class="split" href="cutoff-energy"></a><a href="#_toc/renormalization" class="u"> Renormalization</a></span></span></div></li><li><div id="_toc/effective-field-theory"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#effective-field-theory">Effective field theory</a><span class="hover-metadata"><a class="split" href="effective-field-theory"></a><a href="#_toc/renormalization" class="u"> Renormalization</a><span class="metrics"><span class="wcntr"> 48</span></span></span></span></div></li><li class="has-child"><div id="_toc/yang-mills-theory"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#yang-mills-theory">Yang-Mills theory</a><span class="hover-metadata"><a class="split" href="yang-mills-theory"></a><a href="#_toc/renormalization" class="u"> Renormalization</a><span class="metrics"><span class="wcntr"> 225</span><span class="dcnt"> 2</span></span></span></span></div><ul><li class="has-child"><div id="_toc/yang-mills-existence-and-mass-gap"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#yang-mills-existence-and-mass-gap">Yang-Mills existence and mass gap</a><span class="hover-metadata"><a class="split" href="yang-mills-existence-and-mass-gap"></a><a href="#_toc/yang-mills-theory" class="u"> Yang-Mills theory</a><span class="metrics"><span class="wcntr"> 225</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/wightman-axioms"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#wightman-axioms">Wightman axioms</a><span class="hover-metadata"><a class="split" href="wightman-axioms"></a><a href="#_toc/yang-mills-existence-and-mass-gap" class="u"> Yang-Mills existence and mass gap</a></span></span></div></li></ul></li></ul></li></ul></li></ul><li class="has-child"><div id="_toc/quantum-electrodynamics"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-electrodynamics">Quantum electrodynamics</a><span class="hover-metadata"><a class="split" href="quantum-electrodynamics"></a><a href="#_toc" class="u"> Quantum field theory</a><span class="metrics"><span class="wcntr"> 3k</span><span class="dcnt"> 32</span></span></span></span></div><ul><li class="has-child"><div id="_toc/quantum-electrodynamics-experiment"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-electrodynamics-experiment">Quantum electrodynamics experiment</a><span class="hover-metadata"><a class="split" href="quantum-electrodynamics-experiment"></a><a href="#_toc/quantum-electrodynamics" class="u"> Quantum electrodynamics</a><span class="metrics"><span class="wcntr"> 778</span><span class="dcnt"> 8</span></span></span></span></div><ul><li class="has-child"><div id="_toc/lamb-shift"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#lamb-shift">Lamb shift <span class="meta">(1947)</span></a><span class="hover-metadata"><a class="split" href="lamb-shift"></a><a href="#_toc/quantum-electrodynamics-experiment" class="u"> Quantum electrodynamics experiment</a><span class="metrics"><span class="wcntr"> 524</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/lamb-retherford-experiment"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#lamb-retherford-experiment">Lamb-Retherford experiment <span class="meta">(1947, Lamb shift experiment)</span></a><span class="hover-metadata"><a class="split" href="lamb-retherford-experiment"></a><a href="#_toc/lamb-shift" class="u"> Lamb shift</a><span class="metrics"><span class="wcntr"> 199</span></span></span></span></div></li></ul><li class="has-child"><div id="_toc/electron-magnetic-moment"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#electron-magnetic-moment">Electron magnetic moment</a><span class="hover-metadata"><a class="split" href="electron-magnetic-moment"></a><a href="#_toc/quantum-electrodynamics-experiment" class="u"> Quantum electrodynamics experiment</a><span class="metrics"><span class="wcntr"> 80</span><span class="dcnt"> 3</span></span></span></span></div><ul><li class="has-child"><div id="_toc/anomalous-magnetic-dipole-moment"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#anomalous-magnetic-dipole-moment">Anomalous magnetic dipole moment</a><span class="hover-metadata"><a class="split" href="anomalous-magnetic-dipole-moment"></a><a href="#_toc/electron-magnetic-moment" class="u"> Electron magnetic moment</a><span class="metrics"><span class="wcntr"> 80</span><span class="dcnt"> 2</span></span></span></span></div><ul><li class="has-child"><div id="_toc/anomalous-magnetic-dipole-moment-of-the-electron"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#anomalous-magnetic-dipole-moment-of-the-electron">Anomalous magnetic dipole moment of the electron</a><span class="hover-metadata"><a class="split" href="anomalous-magnetic-dipole-moment-of-the-electron"></a><a href="#_toc/anomalous-magnetic-dipole-moment" class="u"> Anomalous magnetic dipole moment</a><span class="metrics"><span class="wcntr"> 80</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/the-magnetic-moment-of-the-electron-by-kusch-and-foley-1948"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#the-magnetic-moment-of-the-electron-by-kusch-and-foley-1948">The Magnetic Moment of the Electron by Kusch and Foley (1948)</a><span class="hover-metadata"><a class="split" href="the-magnetic-moment-of-the-electron-by-kusch-and-foley-1948"></a><a href="#_toc/anomalous-magnetic-dipole-moment-of-the-electron" class="u"> Anomalous magnetic dipole moment of the electron</a><span class="metrics"><span class="wcntr"> 10</span></span></span></span></div></li></ul></li></ul></li></ul><li class="has-child"><div id="_toc/dirac-equation-vs-quantum-electrodynamics"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#dirac-equation-vs-quantum-electrodynamics">Dirac equation vs quantum electrodynamics</a><span class="hover-metadata"><a class="split" href="dirac-equation-vs-quantum-electrodynamics"></a><a href="#_toc/quantum-electrodynamics-experiment" class="u"> Quantum electrodynamics experiment</a><span class="metrics"><span class="wcntr"> 156</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/the-dirac-equation-does-not-work-for-more-than-one-electron"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#the-dirac-equation-does-not-work-for-more-than-one-electron">The Dirac equation does not work for more than one electron</a><span class="hover-metadata"><a class="split" href="the-dirac-equation-does-not-work-for-more-than-one-electron"></a><a href="#_toc/dirac-equation-vs-quantum-electrodynamics" class="u"> Dirac equation vs quantum electrodynamics</a><span class="metrics"><span class="wcntr"> 58</span></span></span></span></div></li></ul></li></ul><li><div id="_toc/applications-of-quantum-electrodynamics"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#applications-of-quantum-electrodynamics">Applications of quantum electrodynamics</a><span class="hover-metadata"><a class="split" href="applications-of-quantum-electrodynamics"></a><a href="#_toc/quantum-electrodynamics" class="u"> Quantum electrodynamics</a></span></span></div></li><li class="has-child"><div id="_toc/quantum-electrodynamics-lagrangian"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-electrodynamics-lagrangian">Quantum electrodynamics Lagrangian <span class="meta">(QED Lagrangian)</span></a><span class="hover-metadata"><a class="split" href="quantum-electrodynamics-lagrangian"></a><a href="#_toc/quantum-electrodynamics" class="u"> Quantum electrodynamics</a><span class="metrics"><span class="wcntr"> 326</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/derivation-of-the-quantum-electrodynamics-lagrangian"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#derivation-of-the-quantum-electrodynamics-lagrangian">Derivation of the quantum electrodynamics Lagrangian <span class="meta">(Derivation of the QED Lagrangian)</span></a><span class="hover-metadata"><a class="split" href="derivation-of-the-quantum-electrodynamics-lagrangian"></a><a href="#_toc/quantum-electrodynamics-lagrangian" class="u"> Quantum electrodynamics Lagrangian</a><span class="metrics"><span class="wcntr"> 198</span></span></span></span></div></li></ul><li><div id="_toc/what-does-it-mean-that-photons-are-force-carriers-for-electromagnetism"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#what-does-it-mean-that-photons-are-force-carriers-for-electromagnetism">What does it mean that photons are force carriers for electromagnetism?</a><span class="hover-metadata"><a class="split" href="what-does-it-mean-that-photons-are-force-carriers-for-electromagnetism"></a><a href="#_toc/quantum-electrodynamics" class="u"> Quantum electrodynamics</a><span class="metrics"><span class="wcntr"> 254</span></span></span></span></div></li><li><div id="_toc/photon-field"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#photon-field">Photon field</a><span class="hover-metadata"><a class="split" href="photon-field"></a><a href="#_toc/quantum-electrodynamics" class="u"> Quantum electrodynamics</a></span></span></div></li><li><div id="_toc/schwinger-effect"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#schwinger-effect">Schwinger effect</a><span class="hover-metadata"><a class="split" href="schwinger-effect"></a><a href="#_toc/quantum-electrodynamics" class="u"> Quantum electrodynamics</a></span></span></div></li><li class="has-child"><div id="_toc/feynman-diagram"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#feynman-diagram">Feynman diagram</a><span class="hover-metadata"><a class="split" href="feynman-diagram"></a><a href="#_toc/quantum-electrodynamics" class="u"> Quantum electrodynamics</a><span class="metrics"><span class="wcntr"> 75</span><span class="dcnt"> 2</span></span></span></span></div><ul><li><div id="_toc/feynman-diagram-solver"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#feynman-diagram-solver">Feynman diagram solver</a><span class="hover-metadata"><a class="split" href="feynman-diagram-solver"></a><a href="#_toc/feynman-diagram" class="u"> Feynman diagram</a></span></span></div></li><li><div id="_toc/does-the-exact-position-of-vertices-matter-in-feynman-diagrams"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#does-the-exact-position-of-vertices-matter-in-feynman-diagrams">Does the exact position of vertices matter in Feynman diagrams?</a><span class="hover-metadata"><a class="split" href="does-the-exact-position-of-vertices-matter-in-feynman-diagrams"></a><a href="#_toc/feynman-diagram" class="u"> Feynman diagram</a><span class="metrics"><span class="wcntr"> 3</span></span></span></span></div></li></ul><li><div id="_toc/wheeler-feynman-absorber-theory"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#wheeler-feynman-absorber-theory">Wheeler-Feynman absorber theory</a><span class="hover-metadata"><a class="split" href="wheeler-feynman-absorber-theory"></a><a href="#_toc/quantum-electrodynamics" class="u"> Quantum electrodynamics</a><span class="metrics"><span class="wcntr"> 10</span></span></span></span></div></li><li class="has-child"><div id="_toc/cavity-quantum-electrodynamics"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#cavity-quantum-electrodynamics">Cavity quantum electrodynamics</a><span class="hover-metadata"><a class="split" href="cavity-quantum-electrodynamics"></a><a href="#_toc/quantum-electrodynamics" class="u"> Quantum electrodynamics</a><span class="metrics"><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/circuit-quantum-electrodynamics"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#circuit-quantum-electrodynamics">Circuit quantum electrodynamics</a><span class="hover-metadata"><a class="split" href="circuit-quantum-electrodynamics"></a><a href="#_toc/cavity-quantum-electrodynamics" class="u"> Cavity quantum electrodynamics</a></span></span></div></li></ul><li><div id="_toc/positrons-are-electrons-travelling-back-in-time"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#positrons-are-electrons-travelling-back-in-time">Positrons are electrons travelling back in time</a><span class="hover-metadata"><a class="split" href="positrons-are-electrons-travelling-back-in-time"></a><a href="#_toc/quantum-electrodynamics" class="u"> Quantum electrodynamics</a><span class="metrics"><span class="wcntr"> 4</span></span></span></span></div></li><li class="has-child"><div id="_toc/quantum-electrodynamics-bibliography"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-electrodynamics-bibliography">Quantum electrodynamics bibliography</a><span class="hover-metadata"><a class="split" href="quantum-electrodynamics-bibliography"></a><a href="#_toc/quantum-electrodynamics" class="u"> Quantum electrodynamics</a><span class="metrics"><span class="wcntr"> 984</span><span class="dcnt"> 9</span></span></span></span></div><ul><li><div id="_toc/quantum-theory-of-radiation-by-fermi-1932"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-theory-of-radiation-by-fermi-1932">Quantum Theory of Radiation by Fermi (1932)</a><span class="hover-metadata"><a class="split" href="quantum-theory-of-radiation-by-fermi-1932"></a><a href="#_toc/quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a></span></span></div></li><li><div id="_toc/advanced-quantum-mechanics-by-freeman-dyson-1951"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#advanced-quantum-mechanics-by-freeman-dyson-1951">Advanced quantum mechanics by Freeman Dyson (1951)</a><span class="hover-metadata"><a class="split" href="advanced-quantum-mechanics-by-freeman-dyson-1951"></a><a href="#_toc/quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><span class="metrics"><span class="wcntr"> 84</span></span></span></span></div></li><li><div id="_toc/selected-papers-on-quantum-electrodynamics-by-julian-schwinger-1958"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#selected-papers-on-quantum-electrodynamics-by-julian-schwinger-1958">Selected Papers on Quantum Electrodynamics by Julian Schwinger (1958)</a><span class="hover-metadata"><a class="split" href="selected-papers-on-quantum-electrodynamics-by-julian-schwinger-1958"></a><a href="#_toc/quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><span class="metrics"><span class="wcntr"> 11</span></span></span></span></div></li><li class="has-child"><div id="_toc/richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979">Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)</a><span class="hover-metadata"><a class="split" href="richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979"></a><a href="#_toc/quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><span class="metrics"><span class="wcntr"> 823</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/quantum-mechanical-view-of-reality-by-richard-feynman-1983"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-mechanical-view-of-reality-by-richard-feynman-1983">Quantum Mechanical View of Reality by Richard Feynman (1983)</a><span class="hover-metadata"><a class="split" href="quantum-mechanical-view-of-reality-by-richard-feynman-1983"></a><a href="#_toc/richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979" class="u"> Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)</a><span class="metrics"><span class="wcntr"> 176</span></span></span></span></div></li></ul><li><div id="_toc/quantum-electrodynamics-by-lifshitz-et-al-2nd-edition-1982"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-electrodynamics-by-lifshitz-et-al-2nd-edition-1982">Quantum electrodynamics by Lifshitz et al. 2nd edition (1982)</a><span class="hover-metadata"><a class="split" href="quantum-electrodynamics-by-lifshitz-et-al-2nd-edition-1982"></a><a href="#_toc/quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a></span></span></div></li><li><div id="_toc/physics-253a-by-sidney-coleman-1986"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#physics-253a-by-sidney-coleman-1986">Physics 253a by Sidney Coleman (1986)</a><span class="hover-metadata"><a class="split" href="physics-253a-by-sidney-coleman-1986"></a><a href="#_toc/quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a></span></span></div></li><li><div id="_toc/qed-and-the-men-who-made-it-dyson-feynman-schwinger-and-tomonaga-by-silvan-schweber-1994"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#qed-and-the-men-who-made-it-dyson-feynman-schwinger-and-tomonaga-by-silvan-schweber-1994">QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994)</a><span class="hover-metadata"><a class="split" href="qed-and-the-men-who-made-it-dyson-feynman-schwinger-and-tomonaga-by-silvan-schweber-1994"></a><a href="#_toc/quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><span class="metrics"><span class="wcntr"> 48</span></span></span></span></div></li><li><div id="_toc/advanced-quantum-mechanics-ii-by-douglas-gingrich-2004"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#advanced-quantum-mechanics-ii-by-douglas-gingrich-2004">Advanced quantum mechanics II by Douglas Gingrich (2004)</a><span class="hover-metadata"><a class="split" href="advanced-quantum-mechanics-ii-by-douglas-gingrich-2004"></a><a href="#_toc/quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><span class="metrics"><span class="wcntr"> 2</span></span></span></span></div></li></ul></li></ul><li class="has-child"><div id="_toc/weak-interaction"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#weak-interaction">Weak interaction</a><span class="hover-metadata"><a class="split" href="weak-interaction"></a><a href="#_toc" class="u"> Quantum field theory</a><span class="metrics"><span class="wcntr"> 271</span><span class="dcnt"> 9</span></span></span></span></div><ul><li><div id="_toc/electroweak-interaction"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#electroweak-interaction">Electroweak interaction</a><span class="hover-metadata"><a class="split" href="electroweak-interaction"></a><a href="#_toc/weak-interaction" class="u"> Weak interaction</a><span class="metrics"><span class="wcntr"> 15</span></span></span></span></div></li><li class="has-child"><div id="_toc/parity-violation"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#parity-violation">Parity violation</a><span class="hover-metadata"><a class="split" href="parity-violation"></a><a href="#_toc/weak-interaction" class="u"> Weak interaction</a><span class="metrics"><span class="wcntr"> 38</span><span class="dcnt"> 4</span></span></span></span></div><ul><li><div id="_toc/wu-experiment"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#wu-experiment">Wu experiment <span class="meta">(1956)</span></a><span class="hover-metadata"><a class="split" href="wu-experiment"></a><a href="#_toc/parity-violation" class="u"> Parity violation</a></span></span></div></li><li class="has-child"><div id="_toc/cp-violation"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#cp-violation">CP Violation</a><span class="hover-metadata"><a class="split" href="cp-violation"></a><a href="#_toc/parity-violation" class="u"> Parity violation</a><span class="metrics"><span class="dcnt"> 2</span></span></span></span></div><ul><li><div id="_toc/cpt-symmetry"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#cpt-symmetry">CPT symmetry</a><span class="hover-metadata"><a class="split" href="cpt-symmetry"></a><a href="#_toc/cp-violation" class="u"> CP Violation</a></span></span></div></li><li><div id="_toc/strong-cp-problem"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#strong-cp-problem">Strong CP problem</a><span class="hover-metadata"><a class="split" href="strong-cp-problem"></a><a href="#_toc/cp-violation" class="u"> CP Violation</a></span></span></div></li></ul></li></ul><li><div id="_toc/weak-charge"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#weak-charge">Weak charge</a><span class="hover-metadata"><a class="split" href="weak-charge"></a><a href="#_toc/weak-interaction" class="u"> Weak interaction</a></span></span></div></li><li><div id="_toc/w-boson"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#w-boson">W boson</a><span class="hover-metadata"><a class="split" href="w-boson"></a><a href="#_toc/weak-interaction" class="u"> Weak interaction</a></span></span></div></li><li><div id="_toc/z-boson"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#z-boson">Z boson</a><span class="hover-metadata"><a class="split" href="z-boson"></a><a href="#_toc/weak-interaction" class="u"> Weak interaction</a></span></span></div></li></ul><li class="has-child"><div id="_toc/quantum-chromodynamics"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-chromodynamics">Quantum chromodynamics <span class="meta">(QCD)</span></a><span class="hover-metadata"><a class="split" href="quantum-chromodynamics"></a><a href="#_toc" class="u"> Quantum field theory</a><span class="metrics"><span class="wcntr"> 123</span><span class="dcnt"> 11</span></span></span></span></div><ul><li class="has-child"><div id="_toc/quark"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quark">Quark</a><span class="hover-metadata"><a class="split" href="quark"></a><a href="#_toc/quantum-chromodynamics" class="u"> Quantum chromodynamics</a><span class="metrics"><span class="wcntr"> 3</span><span class="dcnt"> 3</span></span></span></span></div><ul><li><div id="_toc/down-quark"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#down-quark">Down quark</a><span class="hover-metadata"><a class="split" href="down-quark"></a><a href="#_toc/quark" class="u"> Quark</a></span></span></div></li><li class="has-child"><div id="_toc/up-quark"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#up-quark">Up quark</a><span class="hover-metadata"><a class="split" href="up-quark"></a><a href="#_toc/quark" class="u"> Quark</a><span class="metrics"><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/why-do-the-up-ad-down-quarks-have-different-masses"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#why-do-the-up-ad-down-quarks-have-different-masses">Why do the up ad down quarks have different masses?</a><span class="hover-metadata"><a class="split" href="why-do-the-up-ad-down-quarks-have-different-masses"></a><a href="#_toc/up-quark" class="u"> Up quark</a></span></span></div></li></ul></li></ul><li><div id="_toc/strange-quark"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#strange-quark">Strange quark</a><span class="hover-metadata"><a class="split" href="strange-quark"></a><a href="#_toc/quantum-chromodynamics" class="u"> Quantum chromodynamics</a></span></span></div></li><li class="has-child"><div id="_toc/gluon"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#gluon">Gluon</a><span class="hover-metadata"><a class="split" href="gluon"></a><a href="#_toc/quantum-chromodynamics" class="u"> Quantum chromodynamics</a><span class="metrics"><span class="wcntr"> 21</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/glueball"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#glueball">Glueball</a><span class="hover-metadata"><a class="split" href="glueball"></a><a href="#_toc/gluon" class="u"> Gluon</a></span></span></div></li></ul><li><div id="_toc/proton-decay"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#proton-decay">Proton decay</a><span class="hover-metadata"><a class="split" href="proton-decay"></a><a href="#_toc/quantum-chromodynamics" class="u"> Quantum chromodynamics</a></span></span></div></li><li><div id="_toc/strong-interaction"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#strong-interaction">Strong interaction</a><span class="hover-metadata"><a class="split" href="strong-interaction"></a><a href="#_toc/quantum-chromodynamics" class="u"> Quantum chromodynamics</a></span></span></div></li><li><div id="_toc/color-charge"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#color-charge">Color charge</a><span class="hover-metadata"><a class="split" href="color-charge"></a><a href="#_toc/quantum-chromodynamics" class="u"> Quantum chromodynamics</a></span></span></div></li><li><div id="_toc/color-confinement"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#color-confinement">Color confinement</a><span class="hover-metadata"><a class="split" href="color-confinement"></a><a href="#_toc/quantum-chromodynamics" class="u"> Quantum chromodynamics</a><span class="metrics"><span class="wcntr"> 47</span></span></span></span></div></li></ul><li class="has-child"><div id="_toc/quantum-field-theory-simulations"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-simulations">Quantum field theory simulations</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-simulations"></a><a href="#_toc" class="u"> Quantum field theory</a><span class="metrics"><span class="wcntr"> 109</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/nielsen-ninomiya-theorem"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#nielsen-ninomiya-theorem">Nielsen-Ninomiya theorem</a><span class="hover-metadata"><a class="split" href="nielsen-ninomiya-theorem"></a><a href="#_toc/quantum-field-theory-simulations" class="u"> Quantum field theory simulations</a><span class="metrics"><span class="wcntr"> 19</span></span></span></span></div></li></ul><li class="has-child"><div id="_toc/infinities-in-quantum-field-theory"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#infinities-in-quantum-field-theory">Infinities in quantum field theory</a><span class="hover-metadata"><a class="split" href="infinities-in-quantum-field-theory"></a><a href="#_toc" class="u"> Quantum field theory</a><span class="metrics"><span class="wcntr"> 13</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/mathematical-consistency-of-quantum-field-theory"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#mathematical-consistency-of-quantum-field-theory">Mathematical consistency of quantum field theory</a><span class="hover-metadata"><a class="split" href="mathematical-consistency-of-quantum-field-theory"></a><a href="#_toc/infinities-in-quantum-field-theory" class="u"> Infinities in quantum field theory</a></span></span></div></li></ul><li class="has-child"><div id="_toc/internal-and-spacetime-symmetries"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#internal-and-spacetime-symmetries">Internal and spacetime symmetries</a><span class="hover-metadata"><a class="split" href="internal-and-spacetime-symmetries"></a><a href="#_toc" class="u"> Quantum field theory</a><span class="metrics"><span class="wcntr"> 126</span><span class="dcnt"> 2</span></span></span></span></div><ul><li><div id="_toc/internal-symmetry"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#internal-symmetry">Internal symmetry</a><span class="hover-metadata"><a class="split" href="internal-symmetry"></a><a href="#_toc/internal-and-spacetime-symmetries" class="u"> Internal and spacetime symmetries</a><span class="metrics"><span class="wcntr"> 2</span></span></span></span></div></li><li><div id="_toc/spacetime-symmetry"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#spacetime-symmetry">Spacetime symmetry</a><span class="hover-metadata"><a class="split" href="spacetime-symmetry"></a><a href="#_toc/internal-and-spacetime-symmetries" class="u"> Internal and spacetime symmetries</a><span class="metrics"><span class="wcntr"> 2</span></span></span></span></div></li></ul><li class="has-child"><div id="_toc/quantum-field-theory-bibliography"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-bibliography">Quantum field theory bibliography</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-bibliography"></a><a href="#_toc" class="u"> Quantum field theory</a><span class="metrics"><span class="wcntr"> 1k</span><span class="dcnt"> 30</span></span></span></span></div><ul><li class="has-child"><div id="_toc/quantum-field-theory-lecture-notes"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-notes">Quantum field theory lecture notes</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-notes"></a><a href="#_toc/quantum-field-theory-bibliography" class="u"> Quantum field theory bibliography</a><span class="metrics"><span class="wcntr"> 318</span><span class="dcnt"> 3</span></span></span></span></div><ul><li><div id="_toc/an-introduction-to-qed-and-qcd-by-jeff-forshaw-1997"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#an-introduction-to-qed-and-qcd-by-jeff-forshaw-1997">An Introduction to QED and QCD by Jeff Forshaw (1997)</a><span class="hover-metadata"><a class="split" href="an-introduction-to-qed-and-qcd-by-jeff-forshaw-1997"></a><a href="#_toc/quantum-field-theory-lecture-notes" class="u"> Quantum field theory lecture notes</a><span class="metrics"><span class="wcntr"> 10</span></span></span></span></div></li><li><div id="_toc/quantum-field-theory-lecture-notes-by-david-tong-2007"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-notes-by-david-tong-2007">Quantum Field Theory lecture notes by David Tong (2007)</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-notes-by-david-tong-2007"></a><a href="#_toc/quantum-field-theory-lecture-notes" class="u"> Quantum field theory lecture notes</a><span class="metrics"><span class="wcntr"> 162</span></span></span></span></div></li><li><div id="_toc/quantum-field-theory-book-by-mark-srednicki-2006"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-book-by-mark-srednicki-2006">Quantum Field Theory book by Mark Srednicki (2006)</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-book-by-mark-srednicki-2006"></a><a href="#_toc/quantum-field-theory-lecture-notes" class="u"> Quantum field theory lecture notes</a><span class="metrics"><span class="wcntr"> 94</span></span></span></span></div></li></ul><li class="has-child"><div id="_toc/quantum-field-theory-lectures"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lectures">Quantum field theory lectures</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lectures"></a><a href="#_toc/quantum-field-theory-bibliography" class="u"> Quantum field theory bibliography</a><span class="metrics"><span class="wcntr"> 515</span><span class="dcnt"> 17</span></span></span></span></div><ul><li><div id="_toc/relativistic-quantum-mechanics-by-apoorva-d-patel-2014"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#relativistic-quantum-mechanics-by-apoorva-d-patel-2014">Relativistic Quantum Mechanics by Apoorva D Patel (2014)</a><span class="hover-metadata"><a class="split" href="relativistic-quantum-mechanics-by-apoorva-d-patel-2014"></a><a href="#_toc/quantum-field-theory-lectures" class="u"> Quantum field theory lectures</a><span class="metrics"><span class="wcntr"> 12</span></span></span></span></div></li><li><div id="_toc/new-revolutions-in-particle-physics-by-leonard-susskind-2009"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#new-revolutions-in-particle-physics-by-leonard-susskind-2009">New Revolutions in Particle Physics by Leonard Susskind (2009)</a><span class="hover-metadata"><a class="split" href="new-revolutions-in-particle-physics-by-leonard-susskind-2009"></a><a href="#_toc/quantum-field-theory-lectures" class="u"> Quantum field theory lectures</a><span class="metrics"><span class="wcntr"> 5</span></span></span></span></div></li><li class="has-child"><div id="_toc/david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute">David Tong's 2009 Quantum Field Theory lectures at the Perimeter Institute</a><span class="hover-metadata"><a class="split" href="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute"></a><a href="#_toc/quantum-field-theory-lectures" class="u"> Quantum field theory lectures</a><span class="metrics"><span class="wcntr"> 35</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/lecture-1"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/lecture-1">Lecture 1</a><span class="hover-metadata"><a class="split" href="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/lecture-1"></a><a href="#_toc/david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute" class="u"> David Tong's 2009 Quantum Field Theory lectures at the Perimeter Institute</a></span></span></div></li></ul><li class="has-child"><div id="_toc/quantum-field-theory-courses-by-tobias-osborne"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-courses-by-tobias-osborne">Quantum field theory courses by Tobias Osborne</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-courses-by-tobias-osborne"></a><a href="#_toc/quantum-field-theory-lectures" class="u"> Quantum field theory lectures</a><span class="metrics"><span class="wcntr"> 463</span><span class="dcnt"> 12</span></span></span></span></div><ul><li class="has-child"><div id="_toc/quantum-field-theory-lecture-by-tobias-osborne-2017"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017">Quantum field theory lecture by Tobias Osborne (2017)</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017"></a><a href="#_toc/quantum-field-theory-courses-by-tobias-osborne" class="u"> Quantum field theory courses by Tobias Osborne</a><span class="metrics"><span class="wcntr"> 439</span><span class="dcnt"> 9</span></span></span></span></div><ul><li><div id="_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-1"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-1">Lecture 1</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-1"></a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><span class="metrics"><span class="wcntr"> 146</span></span></span></span></div></li><li><div id="_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2">Lecture 2</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2"></a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><span class="metrics"><span class="wcntr"> 60</span></span></span></span></div></li><li><div id="_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-3"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-3">Lecture 3</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-3"></a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><span class="metrics"><span class="wcntr"> 129</span></span></span></span></div></li><li><div id="_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-4"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-4">Lecture 4</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-4"></a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><span class="metrics"><span class="wcntr"> 46</span></span></span></span></div></li><li><div id="_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-5"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-5">Lecture 5</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-5"></a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><span class="metrics"><span class="wcntr"> 10</span></span></span></span></div></li><li><div id="_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-8"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-8">Lecture 8</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-8"></a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><span class="metrics"><span class="wcntr"> 1</span></span></span></span></div></li><li><div id="_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-9"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-9">Lecture 9</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-9"></a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><span class="metrics"><span class="wcntr"> 1</span></span></span></span></div></li><li><div id="_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-14"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-14">Lecture 14</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-14"></a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><span class="metrics"><span class="wcntr"> 2</span></span></span></span></div></li><li><div id="_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-15"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-15">Lecture 15</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-15"></a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><span class="metrics"><span class="wcntr"> 2</span></span></span></span></div></li></ul><li class="has-child"><div id="_toc/advanced-quantum-field-theory-lecture-by-tobias-osborne-2017"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#advanced-quantum-field-theory-lecture-by-tobias-osborne-2017">Advanced quantum field theory lecture by Tobias Osborne (2017)</a><span class="hover-metadata"><a class="split" href="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017"></a><a href="#_toc/quantum-field-theory-courses-by-tobias-osborne" class="u"> Quantum field theory courses by Tobias Osborne</a><span class="metrics"><span class="wcntr"> 24</span><span class="dcnt"> 1</span></span></span></span></div><ul><li><div id="_toc/advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2">Lecture 2</a><span class="hover-metadata"><a class="split" href="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2"></a><a href="#_toc/advanced-quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Advanced quantum field theory lecture by Tobias Osborne (2017)</a><span class="metrics"><span class="wcntr"> 3</span></span></span></span></div></li></ul></li></ul></li></ul><li class="has-child"><div id="_toc/quantum-field-theory-book"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-book">Quantum field theory book</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-book"></a><a href="#_toc/quantum-field-theory-bibliography" class="u"> Quantum field theory bibliography</a><span class="metrics"><span class="wcntr"> 232</span><span class="dcnt"> 7</span></span></span></span></div><ul><li><div id="_toc/no-nonsense-quantum-field-theory-by-jakob-schwichtenberg-2020"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#no-nonsense-quantum-field-theory-by-jakob-schwichtenberg-2020">No-Nonsense Quantum Field Theory by Jakob Schwichtenberg (2020)</a><span class="hover-metadata"><a class="split" href="no-nonsense-quantum-field-theory-by-jakob-schwichtenberg-2020"></a><a href="#_toc/quantum-field-theory-book" class="u"> Quantum field theory book</a><span class="metrics"><span class="wcntr"> 48</span></span></span></span></div></li><li><div id="_toc/quantum-field-theory-for-the-gifted-amateur-by-tom-lancaster-2015"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-for-the-gifted-amateur-by-tom-lancaster-2015">Quantum Field Theory for The Gifted Amateur by Tom Lancaster (2015)</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-for-the-gifted-amateur-by-tom-lancaster-2015"></a><a href="#_toc/quantum-field-theory-book" class="u"> Quantum field theory book</a><span class="metrics"><span class="wcntr"> 17</span></span></span></span></div></li><li><div id="_toc/student-friendly-quantum-field-theory-by-robert-d-klauber-2013"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#student-friendly-quantum-field-theory-by-robert-d-klauber-2013">Student Friendly Quantum Field Theory by Robert D Klauber (2013)</a><span class="hover-metadata"><a class="split" href="student-friendly-quantum-field-theory-by-robert-d-klauber-2013"></a><a href="#_toc/quantum-field-theory-book" class="u"> Quantum field theory book</a></span></span></div></li><li><div id="_toc/quantum-field-theory-in-a-nutshell-by-anthony-zee-2010"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-in-a-nutshell-by-anthony-zee-2010">Quantum field theory in a nutshell by Anthony Zee (2010)</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-in-a-nutshell-by-anthony-zee-2010"></a><a href="#_toc/quantum-field-theory-book" class="u"> Quantum field theory book</a><span class="metrics"><span class="wcntr"> 37</span></span></span></span></div></li><li><div id="_toc/problem-book-in-quantum-field-theory-by-voja-radovanovic-2008"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#problem-book-in-quantum-field-theory-by-voja-radovanovic-2008">Problem Book in Quantum Field Theory by Voja Radovanovic (2008)</a><span class="hover-metadata"><a class="split" href="problem-book-in-quantum-field-theory-by-voja-radovanovic-2008"></a><a href="#_toc/quantum-field-theory-book" class="u"> Quantum field theory book</a></span></span></div></li><li><div id="_toc/quantum-field-theory-demystified-by-david-mcmahon-2008"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#quantum-field-theory-demystified-by-david-mcmahon-2008">Quantum Field Theory Demystified by David McMahon (2008)</a><span class="hover-metadata"><a class="split" href="quantum-field-theory-demystified-by-david-mcmahon-2008"></a><a href="#_toc/quantum-field-theory-book" class="u"> Quantum field theory book</a><span class="metrics"><span class="wcntr"> 46</span></span></span></span></div></li><li><div id="_toc/an-introduction-to-quantum-field-theory-by-peskin-and-schroeder-1995"><div class="arrow"><div></div></div><span class="not-arrow"><a href="#an-introduction-to-quantum-field-theory-by-peskin-and-schroeder-1995">An Introduction To Quantum Field Theory by Peskin and Schroeder (1995)</a><span class="hover-metadata"><a class="split" href="an-introduction-to-quantum-field-theory-by-peskin-and-schroeder-1995"></a><a href="#_toc/quantum-field-theory-book" class="u"> Quantum field theory book</a><span class="metrics"><span class="wcntr"> 39</span></span></span></span></div></li></ul></li></ul></li></ul></li></ul></div><div class="h" id="quantum-field"><div class="notnav"><h2><a href="quantum-field">Quantum field</a></h2><span class="hover-meta"> <a class="split" href="quantum-field"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="" class="u"> Quantum field theory</a><a href="#_toc/quantum-field" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="mathematical-formulation-of-quantum-field-theory"><div class="notnav"><h2><a href="mathematical-formulation-of-quantum-field-theory">Mathematical formulation of quantum field theory</a></h2><span class="hover-meta"> <a class="split" href="mathematical-formulation-of-quantum-field-theory"></a><span class="metrics"><span class="wcntr"> Words: 884</span><span class="dcnt"> Articles: 19</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="" class="u"> Quantum field theory</a><a href="#_toc/mathematical-formulation-of-quantum-field-theory" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/mathematical-formulation-of-quantum-field-theory"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_24">TODO holy crap, even this is hard to understand/find a clear definition of.</div><div class="p" id="_25">The <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a>, OK, is a <a href="calculus#partial-differential-equation">partial differential equation</a>, so we can easily understand its definition with basic calculus. We may not be able to solve it efficiently, but at least we understand it.</div><div class="p" id="_26">But what the heck is the mathematical model for a quantum field theory? TODO someone was saying it is equivalent to an infinite set of PDEs somehow. Investigate. Related:<div class="list"><ul id="_27"><li id="_28"><a href="https://www.reddit.com/r/AskPhysics/comments/74qeag/what_is_so_hard_about_qft_after_all/">www.reddit.com/r/AskPhysics/comments/74qeag/what_is_so_hard_about_qft_after_all/</a></li><li id="_29"><a href="https://physics.stackexchange.com/questions/337423/what-are-quantum-fields-mathematically">physics.stackexchange.com/questions/337423/what-are-quantum-fields-mathematically</a></li><li id="_30"><a href="https://physics.stackexchange.com/questions/155608/what-is-a-quantum-field">physics.stackexchange.com/questions/155608/what-is-a-quantum-field</a></li></ul></div></div><div class="p" id="_31">The <a href="#path-integral-formulation">path integral formulation</a> might actually be the most understandable formulation, as shown at <a href="#richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979">Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)</a>.</div><div class="p" id="_32">The formulation of QFT also appears to be a form of infinite-dimentional calculus.</div><div class="p" id="_33"><a href="#quantum-electrodynamics-by-lifshitz-et-al-2nd-edition-1982">Quantum electrodynamics by Lifshitz et al. 2nd edition (1982)</a> chapter 1. "The uncertainty principle in the relativistic case" contains an interesting idea:<div><blockquote id="_34">The foregoing discussion suggests that the theory will not consider the time dependence of particle interaction processes. It will show that in these processes there are no characteristics precisely definable (even within the usual limitations of quantum mechanics); the description of such a process as occurring in the course of time is therefore just as unreal as the classical paths are in non-relativistic quantum mechanics. The only observable quantities are the properties (momenta,<br>polarizations) of free particles: the initial particles which come into interaction, and the final particles which result from the process.</blockquote></div></div><div class="h" id="gauge-theory"><div class="notnav"><h3><a href="gauge-theory">Gauge theory</a></h3><span class="hover-meta"> <a class="split" href="gauge-theory"></a><span class="metrics"><span class="wcntr"> Words: 126</span><span class="dcnt"> Articles: 3</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#mathematical-formulation-of-quantum-field-theory" class="u"> Mathematical formulation of quantum field theory</a><a href="#_toc/gauge-theory" class="toc"></a><a href="https://en.wikipedia.org/wiki/Gauge_theory" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/gauge-theory"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_35">The term and idea was first introduced initialized by <a href="physicist#hermann-weyl">Hermann Weyl</a> when he was working on combining <a href="electromagnetism">electromagnetism</a> and <a href="relativity#general-relativity">general relativity</a> to formulate <a href="relativity#maxwell-s-equations-in-curved-spacetime">Maxwell's equations in curved spacetime</a> in 1918 and published as <a href="physicist#gravity-and-electricity-by-hermann-weyl-1918">Gravity and electricity by Hermann Weyl (1918)</a>. Based on perception that <a href="geometry#unitary-group-of-degree-1"><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mopen">(</span><span class="mord">1</span><span class="mclose">)</span></span></span></span></a> symmetry implies <a href="electromagnetism#charge-conservation">charge conservation</a>. The same idea was later adapted for <a href="#quantum-electrodynamics">quantum electrodynamics</a>, a context in which is has even more impact.</div><div class="h" id="lattice-gauge-theory"><div class="notnav"><h4><a href="lattice-gauge-theory">Lattice gauge theory</a></h4><span class="hover-meta"> <a class="split" href="lattice-gauge-theory"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#gauge-theory" class="u"> Gauge theory</a><a href="#_toc/lattice-gauge-theory" class="toc"></a><a href="https://en.wikipedia.org/wiki/Lattice_gauge_theory" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/lattice-gauge-theory"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="gauge-field"><div class="notnav"><h4><a href="gauge-field">Gauge field</a></h4><span class="hover-meta"> <a class="split" href="gauge-field"></a><span class="metrics"><span class="wcntr"> Words: 17</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#gauge-theory" class="u"> Gauge theory</a><a href="#_toc/gauge-field" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/gauge-field"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_36">A random field you add to make something transform locally the way you want. See e.g.: <a href="#video-deriving-the-qed-lagrangian-by-dietterich-labs-2018">Video 17. "Deriving the qED Lagrangian by Dietterich Labs (2018)"</a>.</div><div class="h" id="gauge-symmetry"><div class="notnav"><h4><a href="gauge-symmetry">Gauge symmetry</a></h4><span class="hover-meta"> <a class="split" href="gauge-symmetry"></a><span class="metrics"><span class="wcntr"> Words: 61</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#gauge-theory" class="u"> Gauge theory</a><a href="#_toc/gauge-symmetry" class="toc"></a><a href="https://en.wikipedia.org/wiki/Gauge_symmetry_(mathematics)" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/gauge-symmetry"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="figure"><figure id="video-lawrence-krauss-explains-gauge-symmetry-by-joe-rogan-2017" class="multiline"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/YP-tPE7WO64" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-lawrence-krauss-explains-gauge-symmetry-by-joe-rogan-2017"><span class="caption-prefix">Video 4. </span></a><div class="title">Lawrence Krauss explains Gauge symmetry by Joe Rogan (2017)</div> <a href="https://www.youtube.com/watch?v=YP-tPE7WO64">Source</a>. <div class="p" id="_37">While most of this is useless as you would expect from the channel, it does give one key idea: you can change charge locally, but things somehow still work out.</div><div class="p" id="_38">And this has something to do with the general intuition of <a href="relativity#special-relativity">special relativity</a> that only local measures make much sense, as evidenced by <a href="relativity#einstein-synchronization">Einstein synchronization</a>.</div></figcaption></figure></div><div class="h" id="fock-space"><div class="notnav"><h3><a href="fock-space">Fock space</a></h3><span class="hover-meta"> <a class="split" href="fock-space"></a><span class="metrics"><span class="wcntr"> Words: 14</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#mathematical-formulation-of-quantum-field-theory" class="u"> Mathematical formulation of quantum field theory</a><a href="#_toc/fock-space" class="toc"></a><a href="https://en.wikipedia.org/wiki/Fock_space" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/fock-space"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_39">Yup, this one Focks you up.</div><div class="figure"><figure id="video-what-s-a-fock-space-by-physics-duck-2023"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/NchdNEo5a48" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-what-s-a-fock-space-by-physics-duck-2023"><span class="caption-prefix">Video 5. </span></a><div class="title">What's a Fock space? by Physics Duck (2023)</div> <a href="https://www.youtube.com/watch?v=NchdNEo5a48">Source</a>. </figcaption></figure></div><div class="h" id="second-quantization"><div class="notnav"><h3><a href="second-quantization">Second quantization</a></h3><span class="hover-meta"> <a class="split" href="second-quantization"></a><span class="metrics"><span class="wcntr"> Words: 93</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#mathematical-formulation-of-quantum-field-theory" class="u"> Mathematical formulation of quantum field theory</a><a href="#_toc/second-quantization" class="toc"></a><a href="https://en.wikipedia.org/wiki/Second_quantization" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/second-quantization"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_40"><a href="https://www.quora.com/How-are-quantum-fields-quantized-to-describe-particles">www.quora.com/How-are-quantum-fields-quantized-to-describe-particles</a></div><div class="p" id="_41">Second quantization also appears to be useful not only for <a href="relativistic-quantum-mechanics">relativistic quantum mechanics</a>, but also for <a href="condensed-matter-physics">condensed matter physics</a>. The reason is that the basis idea is to use the number occupation basis. This basis is:<div class="list"><ul id="_42"><li id="_43">convenient for <a href="">quantum field theory</a> because of <a href="relativistic-quantum-mechanics#particle-creation-and-annihilation">particle creation and annihilation</a> changes the number of particles all the time</li><li id="_44">convenient for <a href="condensed-matter-physics">condensed matter physics</a> because there you have a gazillion particles occupying entire <a href="condensed-matter-physics#electronic-band-theory">energy bands</a></li></ul></div></div><div class="p" id="_45">Bibliography:</div><div class="list"><ul id="_46"><li id="_47"><a href="https://www.youtube.com/watch?v=MVqOfEYzwFY">www.youtube.com/watch?v=MVqOfEYzwFY</a> "How to Visualize Quantum Field Theory" by ZAP Physics (2020). Has <a href="#quantum-field-theory-simulations">1D simulations</a> on a circle. Starts towards the right direction, but is a bit lacking unfortunately, could go deeper.</li></ul></div><div class="h" id="canonical-quantization"><div class="notnav"><h4><a href="canonical-quantization">Canonical quantization</a></h4><span class="hover-meta"> <a class="split" href="canonical-quantization"></a><span class="metrics"><span class="wcntr"> Words: 5</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#second-quantization" class="u"> Second quantization</a><a href="#_toc/canonical-quantization" class="toc"></a><a href="https://en.wikipedia.org/wiki/Canonical_quantization" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/canonical-quantization"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_48">Basically a synonym for <a href="#second-quantization">second quantization</a>.</div><div class="h" id="path-integral-formulation"><div class="notnav"><h3><a href="path-integral-formulation">Path integral formulation</a></h3><span class="hover-meta"> <a class="split" href="path-integral-formulation"></a><span class="metrics"><span class="wcntr"> Words: 131</span><span class="dcnt"> Articles: 3</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#mathematical-formulation-of-quantum-field-theory" class="u"> Mathematical formulation of quantum field theory</a><a href="#_toc/path-integral-formulation" class="toc"></a><a href="https://en.wikipedia.org/wiki/Path_integral_formulation" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/path-integral-formulation"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="quantum-mechanics#equivalent-alternatives-to-the-schrodinger-equation">Equivalent alternatives to the Schrodinger equation</a></span></div></nav></div><div class="p" id="_50">This one might actually be understandable! It is what <a href="richard-feynman">Richard Feynman</a> starts to explain at: <a href="#richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979">Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)</a>.</div><div class="p" id="_51">The difficulty is then proving that the total probability remains at 1, and maybe causality is hard too.</div><div class="p" id="_52">The path integral formulation can be seen as a generalization of the <a href="quantum-mechanics#double-slit-experiment">double-slit experiment</a> to infinitely many slits.</div><div class="p" id="_53">Feynman first stared working it out for <a href="quantum-mechanics#non-relativistic-quantum-mechanics">non-relativistic quantum mechanics</a>, with the relativistic goal in mind, and only later on he attained the relativistic goal.</div><div class="p" id="_54">TODO why intuitively did he take that approach? Likely is makes it easier to add <a href="relativity#special-relativity">special relativity</a>.</div><div class="p" id="_55">This approach more directly suggests the idea that <a href="#quantum-particles-take-all-possible-paths">quantum particles take all possible paths</a>.</div><div class="h" id="quantum-particles-take-all-possible-paths"><div class="notnav"><h4><a href="quantum-particles-take-all-possible-paths">Quantum particles take all possible paths</a></h4><span class="hover-meta"> <a class="split" href="quantum-particles-take-all-possible-paths"></a><span class="metrics"><span class="wcntr"> Words: 22</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#path-integral-formulation" class="u"> Path integral formulation</a><a href="#_toc/quantum-particles-take-all-possible-paths" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-particles-take-all-possible-paths"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_56">As mentioned at: <a href="https://physics.stackexchange.com/questions/212726/a-quantum-particle-moving-from-a-to-b-will-take-every-possible-path-from-a-to-b/212790#212790">physics.stackexchange.com/questions/212726/a-quantum-particle-moving-from-a-to-b-will-take-every-possible-path-from-a-to-b/212790#212790</a>, classical <a href="mechanics#gravity-wave">gravity waves</a> for example also "take all possible paths". This is just what waves look like they are doing.</div><div class="h" id="propagator"><div class="notnav"><h4><a href="propagator">Propagator</a></h4><span class="hover-meta"> <a class="split" href="propagator"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#path-integral-formulation" class="u"> Path integral formulation</a><a href="#_toc/propagator" class="toc"></a><a href="https://en.wikipedia.org/wiki/Propagator" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/propagator"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="infinitely-many-slits-thought-experiment"><div class="notnav"><h4><a href="infinitely-many-slits-thought-experiment">Infinitely many slits thought experiment</a></h4><span class="hover-meta"> <a class="split" href="infinitely-many-slits-thought-experiment"></a><span class="metrics"><span class="wcntr"> Words: 13</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#path-integral-formulation" class="u"> Path integral formulation</a><a href="#_toc/infinitely-many-slits-thought-experiment" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/infinitely-many-slits-thought-experiment"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_57">Thought experiment that illustrates the <a href="#path-integral-formulation">path integral formulation</a> of <a href="">quantum field theory</a>.</div><div class="p" id="_58">Mentioned for example in <a href="#quantum-field-theory-in-a-nutshell-by-anthony-zee-2010">quantum field theory in a nutshell by Anthony Zee (2010)</a> page 8.</div><div class="h" id="renormalization"><div class="notnav"><h3><a href="renormalization">Renormalization</a></h3><span class="hover-meta"> <a class="split" href="renormalization"></a><span class="metrics"><span class="wcntr"> Words: 316</span><span class="dcnt"> Articles: 7</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#mathematical-formulation-of-quantum-field-theory" class="u"> Mathematical formulation of quantum field theory</a><a href="#_toc/renormalization" class="toc"></a><a href="https://en.wikipedia.org/wiki/Renormalization" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/renormalization"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="list"><ul id="_59"><li id="_60"><a href="https://www.quora.com/What-is-renormalization-in-quantum-theory-explained-to-graduated-only-not-doctors/answer/Paul-Mainwood">www.quora.com/What-is-renormalization-in-quantum-theory-explained-to-graduated-only-not-doctors/answer/Paul-Mainwood</a> covers the simpler <a href="condensed-matter-physics#ising-model">Ising model</a> case</li></ul></div><div class="figure"><figure id="video-the-biggest-ideas-in-the-universe-11-renormalization-by-sean-carroll-2020"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/Nm8DRUgmjZc" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-the-biggest-ideas-in-the-universe-11-renormalization-by-sean-carroll-2020"><span class="caption-prefix">Video 6. </span></a><div class="title">The Biggest Ideas in the Universe | 11. Renormalization by <a href="physicist#sean-m-carroll">Sean Carroll</a> (2020)</div> <a href="https://www.youtube.com/watch?v=Nm8DRUgmjZc">Source</a>. Gives a very quick and high level overview of <a href="#renormalization">renormalization</a>. It is not enough to satisfy <a href="ciro-santilli">Ciro Santilli</a> as usual for other Sean Carroll videos, but it goes some way.</figcaption></figure></div><div class="h" id="mass-renormalization"><div class="notnav"><h4><a href="mass-renormalization">Mass renormalization</a></h4><span class="hover-meta"> <a class="split" href="mass-renormalization"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#renormalization" class="u"> Renormalization</a><a href="#_toc/mass-renormalization" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/mass-renormalization"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="renormalization-group"><div class="notnav"><h4><a href="renormalization-group">Renormalization group</a></h4><span class="hover-meta"> <a class="split" href="renormalization-group"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#renormalization" class="u"> Renormalization</a><a href="#_toc/renormalization-group" class="toc"></a><a href="https://en.wikipedia.org/wiki/Renormalization_group" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/renormalization-group"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="cutoff-energy"><div class="notnav"><h4><a href="cutoff-energy">Cutoff energy</a></h4><span class="hover-meta"> <a class="split" href="cutoff-energy"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#renormalization" class="u"> Renormalization</a><a href="#_toc/cutoff-energy" class="toc"></a><a href="https://en.wikipedia.org/wiki/Cutoff_energy" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/cutoff-energy"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="effective-field-theory"><div class="notnav"><h4><a href="effective-field-theory">Effective field theory</a></h4><span class="hover-meta"> <a class="split" href="effective-field-theory"></a><span class="metrics"><span class="wcntr"> Words: 48</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#renormalization" class="u"> Renormalization</a><a href="#_toc/effective-field-theory" class="toc"></a><a href="https://en.wikipedia.org/wiki/Effective_field_theory" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/effective-field-theory"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_61"><a href="https://www.youtube.com/watch?v=WB8r7CU7clk&list=PLUl4u3cNGP60TvpbO5toEWC8y8w51dtvm">www.youtube.com/watch?v=WB8r7CU7clk&list=PLUl4u3cNGP60TvpbO5toEWC8y8w51dtvm</a> by Iain Stewart. Basically starts by explaining how <a href="">quantum field theory</a> is so generic that it is hard to get any numerical results out of it :-)</div><div class="p" id="_62">But in particular, we want to describe those subtheories in a way that we can reach arbitrary precision of the full theory if desired.</div><div class="h" id="yang-mills-theory"><div class="notnav"><h4><a href="yang-mills-theory">Yang-Mills theory</a></h4><span class="hover-meta"> <a class="split" href="yang-mills-theory"></a><span class="metrics"><span class="wcntr"> Words: 225</span><span class="dcnt"> Articles: 2</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#renormalization" class="u"> Renormalization</a><a href="#_toc/yang-mills-theory" class="toc"></a><a href="https://en.wikipedia.org/wiki/Yang–Mills_theory" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/yang-mills-theory"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="yang-mills-existence-and-mass-gap"><div class="notnav"><h5><a href="yang-mills-existence-and-mass-gap">Yang-Mills existence and mass gap</a></h5><span class="hover-meta"> <a class="split" href="yang-mills-existence-and-mass-gap"></a><span class="metrics"><span class="wcntr"> Words: 225</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#yang-mills-theory" class="u"> Yang-Mills theory</a><a href="#_toc/yang-mills-existence-and-mass-gap" class="toc"></a><a href="https://en.wikipedia.org/wiki/Yang–Mills_existence_and_mass_gap" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/yang-mills-existence-and-mass-gap"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="list"><ul id="_63"><li id="_64"><a href="https://www.youtube.com/watch?v=-_qNKbwM_eE">www.youtube.com/watch?v=-_qNKbwM_eE</a> Unsolved: Yang-Mills existence and mass gap by J Knudsen (2019). Gives 10 key points, but the truly hard ones are too quick. He knows the thing though.</li></ul></div><div class="p" id="_65"><div class="figure"><figure id="video-yang-mills-1-by-david-metzler-2011" class="multiline"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/j3fsPHnrgLg" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-yang-mills-1-by-david-metzler-2011"><span class="caption-prefix">Video 7. </span></a><div class="title">Yang-Mills 1 by David Metzler (2011)</div> <a href="https://www.youtube.com/watch?v=j3fsPHnrgLg">Source</a>. <div class="p" id="_66">Playlist: <a href="https://www.youtube.com/watch?v=j3fsPHnrgLg&list=PL613A31A706529585&index=13">www.youtube.com/watch?v=j3fsPHnrgLg&list=PL613A31A706529585&index=13</a></div><div class="p" id="_67">A bit disappointing, too high level, with very few nuggests that are not Googleable withing 5 minutes.</div><div class="p" id="_68">Breakdown:<div class="list"><ul id="_69"><li id="_70">1 <a href="https://www.youtube.com/watch?v=j3fsPHnrgLg">www.youtube.com/watch?v=j3fsPHnrgLg</a>: too basic</li><li id="_71">2 <a href="https://www.youtube.com/watch?v=br6OxCLyqAI?t=569">www.youtube.com/watch?v=br6OxCLyqAI?t=569</a>: mentions <a href="group#group-of-lie-type">groups of Lie type</a> in the context of <a href="group#classification-of-finite-simple-groups">classification of finite simple groups</a>. Each group has a little diagram.</li><li id="_72">3 <a href="https://youtu.be/1baiIxKKQlQ?list=PL613A31A706529585&t=728">youtu.be/1baiIxKKQlQ?list=PL613A31A706529585&t=728</a> the original example of a <a href="geometry#local-symmetry">local symmetry</a> was <a href="relativity#general-relativity">general relativity</a>, and that in that context it can be clearly seen that the local symmetry is what causes "forces" to appear<div class="list"><ul id="_73"><li id="_74"><a href="https://youtu.be/1baiIxKKQlQ?list=PL613A31A706529585&t=933">youtu.be/1baiIxKKQlQ?list=PL613A31A706529585&t=933</a> <a href="geometry#local-symmetry">local symmetry</a> gives a conserved current. In the case of <a href="electromagnetism">electromagnetism</a>, this is electrical current. This was the only worthwhile thing he sad to 2021 Ciro. Summarized at: <a href="geometry#local-symmetries-of-the-lagrangian-imply-conserved-currents">local symmetries of the Lagrangian imply conserved currents</a>.</li></ul></div></li><li id="_75"><div class="p" id="_76">4 <a href="https://youtu.be/5ljKcWm7hoU?list=PL613A31A706529585&t=427">youtu.be/5ljKcWm7hoU?list=PL613A31A706529585&t=427</a> <a href="electromagnetism">electromagnetism</a> has both a global symmetry (<a href="relativity#special-relativity">special relativity</a>) but also <a href="geometry#local-symmetry">local symmetry</a>, which leads to the conservation of charge current and forces.</div><div class="p" id="_77"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-3">lecture 3</a> properly defines a <a href="geometry#local-symmetry">local symmetry</a> in terms of the context of the <a href="mechanics#lagrangian-density">lagrangian density</a>, and explains that the conservation of currents there is basically the statement of <a href="mechanics#noether-s-theorem">Noether's theorem</a> in that context.</div></li></ul></div></div></figcaption></figure></div><div class="figure"><figure id="video-millennium-prize-problem-yang-mills-theory-by-david-gross-2018"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/vMiY7zlBOFI" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-millennium-prize-problem-yang-mills-theory-by-david-gross-2018"><span class="caption-prefix">Video 8. </span></a><div class="title">Millennium Prize Problem: Yang Mills Theory by David Gross (2018)</div> <a href="https://www.youtube.com/watch?v=vMiY7zlBOFI">Source</a>. 2 hour talk at the <a href="university#kavli-institute-for-theoretical-physics">Kavli Institute for Theoretical Physics</a>. Too mathematical, 2021 Ciro can't make much out of it.</figcaption></figure></div></div><div class="figure"><figure id="video-lorenzo-sadun-on-the-yang-mills-and-mass-gap-millennium-problem"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/pCQ9GIqpGBI" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-lorenzo-sadun-on-the-yang-mills-and-mass-gap-millennium-problem"><span class="caption-prefix">Video 9. </span></a><div class="title">Lorenzo Sadun on the "Yang-Mills and Mass Gap" <a href="mathematics#millennium-prize-problems">Millennium problem</a></div>. <a href="https://www.youtube.com/watch?v=pCQ9GIqpGBI">Source</a>. Unknown year. He almost gets there, he's good. Just needed to be a little bit deeper.</figcaption></figure></div><div class="h" id="wightman-axioms"><div class="notnav"><h6><a href="wightman-axioms">Wightman axioms</a></h6><span class="hover-meta"> <a class="split" href="wightman-axioms"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#yang-mills-existence-and-mass-gap" class="u"> Yang-Mills existence and mass gap</a><a href="#_toc/wightman-axioms" class="toc"></a><a href="https://en.wikipedia.org/wiki/Wightman_axioms" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/wightman-axioms"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="quantum-electrodynamics"><div class="notnav"><h2><a href="quantum-electrodynamics">Quantum electrodynamics</a></h2><span class="hover-meta"> <a class="split" href="quantum-electrodynamics"></a><span class="metrics"><span class="wcntr"> Words: 3k</span><span class="dcnt"> Articles: 32</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="" class="u"> Quantum field theory</a><a href="#_toc/quantum-electrodynamics" class="toc"></a><a href="https://en.wikipedia.org/wiki/Quantum_electrodynamics" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/quantum-electrodynamics"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_78">Theory that describes <a href="standard-model#electron">electrons</a> and <a href="photon">photons</a> really well, and <a href="#richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979">as Feynman puts it</a> "accounts very precisely for all physical phenomena we have ever observed, except for gravity and nuclear physics" ("including the laughter of the crowd" ;-)).</div><div class="p" id="_79">Learning it is one of <a href="ciro-santilli">Ciro Santilli</a>'s main intellectual <a href="brain#fetish">fetishes</a>.</div><div class="p" id="_80">While Ciro acknowledges that QED is intrinsically challenging due to the wide range or requirements (<a href="quantum-mechanics">quantum mechanics</a>, <a href="relativity#special-relativity">special relativity</a> and <a href="electromagnetism">electromagnetism</a>), Ciro feels that there is a glaring gap in this moneyless market for a learning material that follows the <a href="religion#middle-way">Middle Way</a> as mentioned at: <a href="ciro-santilli#the-missing-link-between-basic-and-advanced">the missing link between basic and advanced</a>. <a href="#richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979">Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)</a> is one of the best attempts so far, but it falls a bit too close to the superficial side of things, if only Feynman hadn't assumed that the audience doesn't know any mathematics...</div><div class="p" id="_81">The funny thing is that when <a href="ciro-santilli#ciro-santilli-s-mother">Ciro Santilli's mother</a> retired, learning it (or as she put it: "how photons and electrons interact") was also one of her retirement plans. She is a pharmacist by training, and doesn't know much <a href="mathematics">mathematics</a>, and her <a href="linguistics#english-language">English</a> was <a href="cirism#having-more-than-one-natural-language-is-bad-for-the-world">somewhat limited</a>. Oh, she also wanted to learn how <a href="taxonomy#photosynthesis">photosynthesis</a> works (possibly not fully understood by science as that time, 2020). Ambitious old lady!!!</div><div class="p" id="_82">Experiments: <a href="#quantum-electrodynamics-experiment">quantum electrodynamics experiments</a>.</div><div class="p" id="_83">Combines <a href="relativity#special-relativity">special relativity</a> with more classical <a href="quantum-mechanics">quantum mechanics</a>, but further generalizing the <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a>, which also does that: <a href="#dirac-equation-vs-quantum-electrodynamics">Dirac equation vs quantum electrodynamics</a>. The name "relativistic" likely doesn't need to appear on the title of QED because <a href="relativity#maxwell-s-equations-require-special-relativity">Maxwell's equations require special relativity</a>, so just having "electro-" in the title is enough.</div><div class="p" id="_84">Before QED, the most advanced theory was that of the <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a>, which was already relativistic but TODO what was missing there exactly?</div><div class="p" id="_85">As summarized at: <a href="https://youtube.com/watch?v=_AZdvtf6hPU?t=305">youtube.com/watch?v=_AZdvtf6hPU?t=305</a> Quantum Field Theory lecture at the African Summer Theory Institute 1 of 4 by Anthony Zee (2004):<div class="list"><ul id="_86"><li id="_87">classical mechanics describes large and slow objects</li><li id="_88">special relativity describes large and fast objects (they are getting close to the speed of light, so we have to consider relativity)</li><li id="_89">classical <a href="quantum-mechanics">quantum mechanics</a> describes small and slow objects.</li><li id="_90">QED describes objects that are both small and fast</li></ul></div></div><div class="p" id="_91">That video also mentions the interesting idea that:<div class="list"><ul id="_92"><li id="_93">in special relativity, we have the <a href="relativity#mass-energy-equivalence">mass-energy equivalence</a></li><li id="_94">in quantum mechanics, thinking along the <a href="quantum-mechanics#time-energy-uncertainty-principle">time-energy uncertainty principle</a>, <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Δ</span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">t</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></li></ul></div>Therefore, for small timescales, energy can vary a lot. But mass is equivalent to energy. Therefore, for small time scale, particles can appear and disappear wildly.</div><div class="p" id="_95">QED is the first <a href="">quantum field theory</a> fully developed. That framework was later extended to also include the <a href="#weak-interaction">weak interaction</a> and <a href="#strong-interaction">strong interaction</a>. As a result, it is perhaps easier to just <a href="google">Google</a> for "Quantum Field Theory" if you want to learn QED, since QFT is more general and has more resources available generally.</div><div class="p" id="_96">Like in more general quantum field theory, there is on field for each particle type. In quantum field theory, there are only two fields to worry about:<div class="list"><ul id="_97"><li id="_98"><a href="photon">photon</a> field</li><li id="_99"><a href="electromagnetism">electromagnetism</a> field</li></ul></div></div><div class="figure"><figure id="video-lecture-01-overview-of-quantum-field-theory-by-markus-luty-2013"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/EzfFklLqDjA" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-lecture-01-overview-of-quantum-field-theory-by-markus-luty-2013"><span class="caption-prefix">Video 10. </span></a><div class="title">Lecture 01 | Overview of Quantum Field Theory by Markus Luty (2013)</div> <a href="https://www.youtube.com/watch?v=EzfFklLqDjA">Source</a>. This takes quite a direct approach, one cool thing he says is how we have to be careful with adding special relativity to the <a href="quantum-mechanics#schrodinger-equation">Schrödinger equation</a> to avoid faster-than-light information.</figcaption></figure></div><div class="p"><b><span title="Tags" class="fa-solid-900 icon"></span> Tagged</b><div class="list"><ul><li><a href="nobel-prize#1965-nobel-prize-in-physics">1965 Nobel Prize in Physics</a></li></ul></div></div><div class="h" id="quantum-electrodynamics-experiment"><div class="notnav"><h3><a href="quantum-electrodynamics-experiment">Quantum electrodynamics experiment</a></h3><span class="hover-meta"> <a class="split" href="quantum-electrodynamics-experiment"></a><span class="metrics"><span class="wcntr"> Words: 778</span><span class="dcnt"> Articles: 8</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics" class="u"> Quantum electrodynamics</a><a href="#_toc/quantum-electrodynamics-experiment" class="toc"></a><a href="https://en.wikipedia.org/wiki/Quantum_electrodynamics_experiment" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/quantum-electrodynamics-experiment"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_100">Experiments explained by QED but not by the <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a>:<div class="list"><ul id="_101"><li id="_102"><a href="#lamb-shift">Lamb shift</a>: by far the most famous one</li><li id="_103"><a href="quantum-mechanics#hyperfine-structure">hyperfine structure</a> TODO confirm</li><li id="_104"><a href="#anomalous-magnetic-dipole-moment-of-the-electron">anomalous magnetic dipole moment of the electron</a></li></ul></div></div><div class="h" id="lamb-shift"><div class="notnav"><h4><a href="lamb-shift">Lamb shift <span class="meta">(1947)</span></a></h4><span class="hover-meta"> <a class="split" href="lamb-shift"></a><span class="metrics"><span class="wcntr"> Words: 524</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-experiment" class="u"> Quantum electrodynamics experiment</a><a href="#_toc/lamb-shift" class="toc"></a><a href="https://en.wikipedia.org/wiki/Lamb_shift" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/lamb-shift"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="physics#the-most-important-physics-experiments">The most important physics experiments</a></span></div></nav></div><div class="p" id="_107">2s/2p energy split in the <a href="quantum-mechanics#hydrogen-emission-spectrum">hydrogen emission spectrum</a>, not predicted by the <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a>, but explained by <a href="#quantum-electrodynamics">quantum electrodynamics</a>, which is one of the first great triumphs of that theory.</div><div class="p" id="_108">Note that for atoms with multiple electrons, 2s/2p shifts are expected: <a href="quantum-mechanics#why-does-2s-have-less-energy-than-1s-if-they-have-the-same-principal-quantum-number">Why does 2s have less energy than 1s if they have the same principal quantum number?</a>. The surprise was observing that on <a href="chemistry#hydrogen">hydrogen</a> which only has one <a href="standard-model#electron">electron</a>. </div><div class="p" id="_109">Initial experiment: <a href="#lamb-retherford-experiment">Lamb-Retherford experiment</a>.</div><div class="p" id="_110">On the return from the train from the <a href="physics#shelter-island-conference">Shelter Island Conference</a> in <a href="united-states#new-york">New York</a>, <a href="physicist#hans-bethe">Hans Bethe</a> managed to do a <a href="relativity">non-relativistic</a> calculation of the <a href="#lamb-shift">Lamb shift</a>. He then published as The Electromagnetic Shift of Energy Levels by Hans Bethe (1947) which is still paywalled as of 2021, <a href="education#academic-publishing">fuck me</a>: <a href="https://journals.aps.org/pr/abstract/10.1103/PhysRev.72.339">journals.aps.org/pr/abstract/10.1103/PhysRev.72.339</a> by <a href="physics#physical-review">Physical Review</a>.</div><div class="p" id="_111">The Electromagnetic Shift of Energy Levels <a href="physicist#freeman-dyson">Freeman Dyson</a> (1948) published on <a href="physics#physical-review">Physical Review</a> is apparently a <a href="relativity">relativistic</a> analysis of the same: <a href="https://journals.aps.org/pr/abstract/10.1103/PhysRev.73.617">journals.aps.org/pr/abstract/10.1103/PhysRev.73.617</a> also paywalled as of 2021.</div><div class="p" id="_112">TODO how do the infinities show up, and how did people solve them?</div><div class="figure"><figure id="video-lamb-shift-by-dr-nissar-ahmad-2020"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/jPKEuiUNJIk" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-lamb-shift-by-dr-nissar-ahmad-2020"><span class="caption-prefix">Video 11. </span></a><div class="title"><a href="#lamb-shift">Lamb shift</a> by Dr. Nissar Ahmad (2020)</div> <a href="https://www.youtube.com/watch?v=jPKEuiUNJIk">Source</a>. Whiteboard Lecture about the phenomena, includes description of the experiment. Seems quite good.</figcaption></figure></div><div class="figure"><figure id="video-murray-gell-mann-the-race-to-calculate-the-relativistic-lamb-shift-by-web-of-stories-1997"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/WcyMfgj9psQ" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-murray-gell-mann-the-race-to-calculate-the-relativistic-lamb-shift-by-web-of-stories-1997"><span class="caption-prefix">Video 12. </span></a><div class="title"><a href="physicist#murray-gell-mann">Murray Gell-Mann</a> - The race to calculate the relativistic <a href="#lamb-shift">Lamb shift</a> by <a href="science#web-of-stories">Web of Stories</a> (1997)</div> <a href="https://www.youtube.com/watch?v=WcyMfgj9psQ">Source</a>. Quick historical overview. Mentions that <a href="richard-feynman">Richard Feynman</a> and <a href="physicist#julian-schwinger">Julian Schwinger</a> were using <a href="#mass-renormalization">mass renormalization</a> and cancellation if infinities. He says that French and Weisskopf actually managed to do the correct calculations first with a less elegant method.</figcaption></figure></div><div class="p" id="_113"><a href="https://www.mdpi.com/2624-8174/2/2/8/pdf">www.mdpi.com/2624-8174/2/2/8/pdf</a> History and Some Aspects of the Lamb Shift by G. Jordan Maclay (2019)</div><div class="figure"><figure id="video-freeman-dyson-the-lamb-shift-by-web-of-stories-1998" class="multiline"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/062GN3RdH1c" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-freeman-dyson-the-lamb-shift-by-web-of-stories-1998"><span class="caption-prefix">Video 13. </span></a><div class="title">Freeman Dyson - The Lamb shift by <a href="science#web-of-stories">Web of Stories</a> (1998)</div> <a href="https://www.youtube.com/watch?v=062GN3RdH1c">Source</a>. <div class="p" id="_114">Mentions that he moved to the <a href="united-states">USA</a> from the <a href="united-kingdom">United Kingdom</a> specifically because great experiments were being carried at <a href="university#columbia-university">Columbia University</a>, which is where the <a href="#lamb-retherford-experiment">Lamb-Retherford experiment</a> was done, and that <a href="physicist#isidor-isaac-rabi">Isidor Isaac Rabi</a> was the head at the time.</div><div class="p" id="_115">He then explains <a href="#mass-renormalization">mass renormalization</a> briefly: instead of calculating from scratch, you just compare the raw electron to the bound electron and take the difference. Both of those have infinities in them, but the difference between them cancels out those infinities.</div></figcaption></figure></div><div class="figure"><figure id="video-hans-bethe-the-lamb-shift-1996" class="multiline"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/YP6TGj-yL7Y" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-hans-bethe-the-lamb-shift-1996"><span class="caption-prefix">Video 14. </span></a><div class="title"><a href="physicist#hans-bethe">Hans Bethe</a> - The Lamb shift (1996)</div> <a href="https://www.youtube.com/watch?v=YP6TGj-yL7Y">Source</a>. <div class="p" id="_116">Ahh, Hans is so old in that video, it is sad to see. He did live a lot tough. Mentions that the shift is of about 1000 MHz.</div><div class="p" id="_117">The following video: <a href="https://www.youtube.com/watch?v=vZvQg3bkV7s">www.youtube.com/watch?v=vZvQg3bkV7s</a> Hans Bethe - Calculating the Lamb shift.</div></figcaption></figure></div><div class="figure"><figure id="video-lamb-shift-by-vidya-mitra-2018"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/-0DDUyR0200" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-lamb-shift-by-vidya-mitra-2018"><span class="caption-prefix">Video 15. </span></a><div class="title"><a href="#lamb-shift">Lamb shift</a> by Vidya-mitra (2018)</div> <a href="https://www.youtube.com/watch?v=-0DDUyR0200">Source</a>. </figcaption></figure></div><div class="h" id="lamb-retherford-experiment"><div class="notnav"><h5><a href="lamb-retherford-experiment">Lamb-Retherford experiment <span class="meta">(1947, Lamb shift experiment)</span></a></h5><span class="hover-meta"> <a class="split" href="lamb-retherford-experiment"></a><span class="metrics"><span class="wcntr"> Words: 199</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#lamb-shift" class="u"> Lamb shift</a><a href="#_toc/lamb-retherford-experiment" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/lamb-retherford-experiment"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="nobel-prize#1955-nobel-prize-in-physics">1955 Nobel Prize in Physics</a></span></div></nav></div><div class="p" id="_121">Published as "Fine Structure of the Hydrogen Atom by a Microwave Method" by <a href="physicist#willis-lamb">Willis Lamb</a> and Robert Retherford (1947) on <a href="physics#physical-review">Physical Review</a>. This one actually has <a href="education#open-access">open accesses</a> as of 2021, miracle! <a href="https://journals.aps.org/pr/pdf/10.1103/PhysRev.72.241">journals.aps.org/pr/pdf/10.1103/PhysRev.72.241</a></div><div class="p" id="_122"><a href="photon#microwave">Microwave</a> technology was developed in <a href="science#world-war-ii">World War II</a> for <a href="telecommunication#radar">radar</a>, notably at the <a href="university#mit-radiation-laboratory">MIT Radiation Laboratory</a>. Before that, people were using much higher frequencies such as the <a href="photon#visible-spectrum">visible spectrum</a>. But to detect small energy differences, you need to look into longer wavelengths.</div><div class="p" id="_123">This experiment was fundamental to the development of <a href="#quantum-electrodynamics">quantum electrodynamics</a>. As mentioned at <a href="genius-richard-feynman-and-modern-physics-by-james-gleick-1994">Genius: Richard Feynman and Modern Physics by James Gleick (1994)</a> chapter "Shrinking the infinities", before the experiment, people already knew that trying to add <a href="electromagnetism">electromagnetism</a> to the <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a> led to <a href="#infinities-in-quantum-field-theory">infinities</a> using previous methods, and something needed to change urgently. However for the first time now the theorists had one precise number to try and hack their formulas to reach, not just a philosophical debate about infinities, and this led to major breakthroughs. The same book also describes the experiment briefly as:<div><blockquote id="_124">Willis Lamb had just shined a beam of microwaves onto a hot wisp of hydrogen blowing from an oven.</blockquote></div></div><div class="p" id="_125">It is two pages and a half long.</div><div class="p" id="_126">They were at <a href="university#columbia-university">Columbia University</a> in the <a href="university#columbia-radiation-laboratory">Columbia Radiation Laboratory</a>. Robert was Willis' graduate student.</div><div class="p" id="_127">Previous less experiments had already hinted at this effect, but they were too imprecise to be sure.</div><div class="h" id="electron-magnetic-moment"><div class="notnav"><h4><a href="electron-magnetic-moment">Electron magnetic moment</a></h4><span class="hover-meta"> <a class="split" href="electron-magnetic-moment"></a><span class="metrics"><span class="wcntr"> Words: 80</span><span class="dcnt"> Articles: 3</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-experiment" class="u"> Quantum electrodynamics experiment</a><a href="#_toc/electron-magnetic-moment" class="toc"></a><a href="https://en.wikipedia.org/wiki/Electron_magnetic_moment" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/electron-magnetic-moment"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="anomalous-magnetic-dipole-moment"><div class="notnav"><h5><a href="anomalous-magnetic-dipole-moment">Anomalous magnetic dipole moment</a></h5><span class="hover-meta"> <a class="split" href="anomalous-magnetic-dipole-moment"></a><span class="metrics"><span class="wcntr"> Words: 80</span><span class="dcnt"> Articles: 2</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#electron-magnetic-moment" class="u"> Electron magnetic moment</a><a href="#_toc/anomalous-magnetic-dipole-moment" class="toc"></a><a href="https://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/anomalous-magnetic-dipole-moment"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="anomalous-magnetic-dipole-moment-of-the-electron"><div class="notnav"><h6><a href="anomalous-magnetic-dipole-moment-of-the-electron">Anomalous magnetic dipole moment of the electron</a></h6><span class="hover-meta"> <a class="split" href="anomalous-magnetic-dipole-moment-of-the-electron"></a><span class="metrics"><span class="wcntr"> Words: 80</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#anomalous-magnetic-dipole-moment" class="u"> Anomalous magnetic dipole moment</a><a href="#_toc/anomalous-magnetic-dipole-moment-of-the-electron" class="toc"></a><a href="https://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment#Electron" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/anomalous-magnetic-dipole-moment-of-the-electron"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="nobel-prize#1955-nobel-prize-in-physics">1955 Nobel Prize in Physics</a></span></div></nav></div><div class="p" id="_129"><a href="#richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979">Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)</a> mentions it several times.</div><div class="p" id="_130">This was one of the first two great successes of <a href="#quantum-electrodynamics">quantum electrodynamics</a>, the other one being the <a href="#lamb-shift">Lamb shift</a>.</div><div class="p" id="_131">In <a href="https://youtu.be/UKbp85zpdcY?t=52">youtu.be/UKbp85zpdcY?t=52</a> from <a href="physicist#freeman-dyson-web-of-stories-interview-1998">freeman Dyson Web of Stories interview (1998)</a> Dyson mentions that the original key experiment was from Kusch and Foley from <a href="university#columbia-university">Columbia University</a>, and that in 1948, <a href="physicist#julian-schwinger">Julian Schwinger</a> reached the correct value from his calculations.</div><div class="p" id="_132">Apparently first published at <a href="#the-magnetic-moment-of-the-electron-by-kusch-and-foley-1948">The Magnetic Moment of the Electron by Kusch and Foley (1948)</a>.</div><div class="p" id="_133">Bibliography:<div class="list"><ul id="_134"><li id="_135"><a href="https://www.youtube.com/watch?v=Ix-3LQhElvU">www.youtube.com/watch?v=Ix-3LQhElvU</a> Anomalous Magnetic Moment Of The Electron | One Loop Quantum Correction | Quantum Electrodynamics by <a href="particle-physics#dietterich-labs">Dietterich Labs</a> (2019)</li></ul></div></div><div class="h" id="the-magnetic-moment-of-the-electron-by-kusch-and-foley-1948"><div class="notnav"><h6 data-level="7"><a href="the-magnetic-moment-of-the-electron-by-kusch-and-foley-1948">The Magnetic Moment of the Electron by Kusch and Foley (1948)</a></h6><span class="hover-meta"> <a class="split" href="the-magnetic-moment-of-the-electron-by-kusch-and-foley-1948"></a><span class="metrics"><span class="wcntr"> Words: 10</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#anomalous-magnetic-dipole-moment-of-the-electron" class="u"> Anomalous magnetic dipole moment of the electron</a><a href="#_toc/the-magnetic-moment-of-the-electron-by-kusch-and-foley-1948" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/the-magnetic-moment-of-the-electron-by-kusch-and-foley-1948"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="nobel-prize#1955-nobel-prize-in-physics">1955 Nobel Prize in Physics</a></span></div></nav></div><div class="p" id="_137">Published on <a href="physics#physical-review">Physical Review</a> by <a href="physicist#polykarp-kusch">Polykarp Kusch</a> and Foley.</div><div class="p" id="_138"><a href="https://journals.aps.org/pr/abstract/10.1103/PhysRev.74.250">journals.aps.org/pr/abstract/10.1103/PhysRev.74.250</a>, paywall as of 2021.</div><div class="h" id="dirac-equation-vs-quantum-electrodynamics"><div class="notnav"><h4><a href="dirac-equation-vs-quantum-electrodynamics">Dirac equation vs quantum electrodynamics</a></h4><span class="hover-meta"> <a class="split" href="dirac-equation-vs-quantum-electrodynamics"></a><span class="metrics"><span class="wcntr"> Words: 156</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-experiment" class="u"> Quantum electrodynamics experiment</a><a href="#_toc/dirac-equation-vs-quantum-electrodynamics" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/dirac-equation-vs-quantum-electrodynamics"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a></span></div></nav></div><div class="p" id="_140">TODO: in high level terms, why is QED more general than just solving the <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a>, and therefore explaining <a href="#quantum-electrodynamics-experiment">quantum electrodynamics experiments</a>?</div><div class="p" id="_141">Also, is it just a bunch of <a href="calculus#differential-equation">differential equation</a> (like the <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a> itself), or does it have some other more complicated mathematical formulation, as seems to be the case? Why do we need something more complicated than </div><div class="p" id="_142">The main high level insight seems to be that <a href="#the-dirac-equation-does-not-work-for-more-than-one-electron">The Dirac equation does not work for more than one electron</a>.</div><div class="p" id="_143">Bibliography:<div class="list"><ul id="_144"><li id="_145"><a href="https://physics.stackexchange.com/questions/101307/dirac-equation-in-qft-vs-relativistic-qm">physics.stackexchange.com/questions/101307/dirac-equation-in-qft-vs-relativistic-qm</a></li><li id="_146"><a href="https://physics.stackexchange.com/questions/44188/what-is-the-relativistic-particle-in-a-box/44309#44309">physics.stackexchange.com/questions/44188/what-is-the-relativistic-particle-in-a-box/44309#44309</a> says:<div><blockquote id="_147">By several reasons explained in textbooks, the Dirac equation is not a valid wavefunction equation. You can solve it and find solutions, but those solutions cannot be interpreted as wavefunctions for a particle</blockquote></div></li><li id="_148"><a href="https://physics.stackexchange.com/questions/64206/why-is-the-dirac-equation-not-used-for-calculations">physics.stackexchange.com/questions/64206/why-is-the-dirac-equation-not-used-for-calculations</a></li><li id="_149"><a href="https://www.physicsforums.com/threads/is-diracs-equation-still-useful-after-qed-is-developed.663994/">www.physicsforums.com/threads/is-diracs-equation-still-useful-after-qed-is-developed.663994/</a></li></ul></div></div><div class="h" id="the-dirac-equation-does-not-work-for-more-than-one-electron"><div class="notnav"><h5><a href="the-dirac-equation-does-not-work-for-more-than-one-electron">The Dirac equation does not work for more than one electron</a></h5><span class="hover-meta"> <a class="split" href="the-dirac-equation-does-not-work-for-more-than-one-electron"></a><span class="metrics"><span class="wcntr"> Words: 58</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#dirac-equation-vs-quantum-electrodynamics" class="u"> Dirac equation vs quantum electrodynamics</a><a href="#_toc/the-dirac-equation-does-not-work-for-more-than-one-electron" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/the-dirac-equation-does-not-work-for-more-than-one-electron"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_150">TODO understand in detail.</div><div class="p" id="_151"><a href="#advanced-quantum-mechanics-by-freeman-dyson-1951">Advanced quantum mechanics by Freeman Dyson (1951)</a> mentions:<div><blockquote id="_152">A Relativistic Quantum Theory of a Finite Number of Particles is Impossible.</blockquote></div></div><div class="p" id="_153"><a href="science#atom-2007-mini-series-episode-3">Atom 2007 Mini Series episode 3</a>:<div><blockquote id="_154">[The <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a>] could only describe a single electron. It fails completely to explain what happens when there is more than one electron present. What was needed was a new theory. A theory which explains how electrons interact with each other. </blockquote></div></div><div class="h" id="applications-of-quantum-electrodynamics"><div class="notnav"><h3><a href="applications-of-quantum-electrodynamics">Applications of quantum electrodynamics</a></h3><span class="hover-meta"> <a class="split" href="applications-of-quantum-electrodynamics"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics" class="u"> Quantum electrodynamics</a><a href="#_toc/applications-of-quantum-electrodynamics" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/applications-of-quantum-electrodynamics"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="list"><ul id="_155"><li id="_156"><a href="https://www.quora.com/What-are-some-engineering-applications-of-QED-or-QCD-quantum-field-theories">www.quora.com/What-are-some-engineering-applications-of-QED-or-QCD-quantum-field-theories</a></li><li id="_157"><a href="physics#relativistic-quantum-chemistry">relativistic quantum chemistry</a></li></ul></div><div class="p"><b><span title="Tags" class="fa-solid-900 icon"></span> Tagged</b><div class="list"><ul><li><a href="physics#relativistic-quantum-chemistry">Relativistic quantum chemistry</a></li></ul></div></div><div class="h" id="quantum-electrodynamics-lagrangian"><div class="notnav"><h3><a href="quantum-electrodynamics-lagrangian">Quantum electrodynamics Lagrangian <span class="meta">(QED Lagrangian)</span></a></h3><span class="hover-meta"> <a class="split" href="quantum-electrodynamics-lagrangian"></a><span class="metrics"><span class="wcntr"> Words: 326</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics" class="u"> Quantum electrodynamics</a><a href="#_toc/quantum-electrodynamics-lagrangian" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-electrodynamics-lagrangian"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_159"><div class="math" id="_160"><div><div class="equation"><div><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathcal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight">QED</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0812em;vertical-align:-0.25em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8312em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span></span><span style="top:-3.2634em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1389em;"><span class="mord">ˉ</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em;"><span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">i</span><span class="mord">ℏ</span><span class="mord mathnormal">c</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">D</span></span><span class="mspace" style="margin-right:-0.1667em;"></span><span class="mspace" style="margin-right:-0.1667em;"></span><span class="mspace" style="margin-right:-0.1667em;"></span><span class="mspace" style="margin-right:-0.1667em;"></span><span class="mord">/</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord mathnormal">m</span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.3262em;vertical-align:-0.4811em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">4</span><span class="mord mtight"><span class="mord mathnormal mtight">μ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.4811em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.06366em;">μν</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.06366em;">μν</span></span></span></span></span></span></span></span></span></span></span></span></div><div class="number"><a href="#_160">(1)</a></div></div></div></div>where:<div class="list"><ul id="_161"><li id="_162"><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span></span></span></span> is the <a href="electromagnetism#electromagnetic-tensor">electromagnetic tensor</a></li></ul></div></div><div class="p" id="_163">Note that this is the sum of the:<div class="list"><ul id="_164"><li id="_165"><a href="relativistic-quantum-mechanics#dirac-lagrangian">Dirac Lagrangian</a>, which only describes the "inertia of bodies" part of the equation</li><li id="_166">the <a href="electromagnetism">electromagnetic</a> interaction term <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3262em;vertical-align:-0.4811em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">4</span><span class="mord mtight"><span class="mord mathnormal mtight">μ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.4811em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.06366em;">μν</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.06366em;">μν</span></span></span></span></span></span></span></span></span></span></span></span>, which describes term describes forces</li></ul></div>Note that the relationship between <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span></span></span></span> and <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span></span></span></span> is not explicit. However, if we knew what type of particle we were talking about, e.g. <a href="standard-model#electron">electron</a>, then the knowledge of <a href="linguistics#psi-greek">psi</a> would also give the charge distribution and therefore <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span></span></span></span></div><div class="p" id="_167">As mentioned at the beginning of <a href="#quantum-field-theory-lecture-notes-by-david-tong-2007">Quantum Field Theory lecture notes by David Tong (2007)</a>:<div class="list"><ul id="_168"><li id="_169">by "<a href="mechanics#lagrangian">Lagrangian</a>" we mean Lagrangian density</li><li id="_170">the <a href="mechanics#generalized-coordinate">generalized coordinates</a> of the Lagrangian are fields</li></ul></div></div><div class="figure"><figure id="video-particle-physics-is-founded-on-this-principle-by-physics-with-elliot-2022"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/I4CjewbJgRQ" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-particle-physics-is-founded-on-this-principle-by-physics-with-elliot-2022"><span class="caption-prefix">Video 16. </span></a><div class="title">Particle Physics is Founded on This Principle! by Physics with Elliot (2022)</div> <a href="https://www.youtube.com/watch?v=I4CjewbJgRQ">Source</a>. </figcaption></figure></div><div class="h" id="derivation-of-the-quantum-electrodynamics-lagrangian"><div class="notnav"><h4><a href="derivation-of-the-quantum-electrodynamics-lagrangian">Derivation of the quantum electrodynamics Lagrangian <span class="meta">(Derivation of the QED Lagrangian)</span></a></h4><span class="hover-meta"> <a class="split" href="derivation-of-the-quantum-electrodynamics-lagrangian"></a><span class="metrics"><span class="wcntr"> Words: 198</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-lagrangian" class="u"> Quantum electrodynamics Lagrangian</a><a href="#_toc/derivation-of-the-quantum-electrodynamics-lagrangian" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/derivation-of-the-quantum-electrodynamics-lagrangian"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_172">Like the rest of the <a href="standard-model#standard-model-lagrangian">Standard Model Lagrangian</a>, this can be split into two parts:<div class="list"><ul id="_173"><li id="_174"><a href="#spacetime-symmetry">spacetime symmetry</a>: reaches the <a href="relativistic-quantum-mechanics#derivation-of-the-dirac-equation">derivation of the Dirac equation</a>, but has no interactions</li><li id="_175">add the <a href="geometry#unitary-group-of-degree-1"><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mopen">(</span><span class="mord">1</span><span class="mclose">)</span></span></span></span></a> <a href="#internal-symmetry">internal symmetry</a> to add interactions, which reaches the full equation</li></ul></div></div><div class="figure"><figure id="video-deriving-the-qed-lagrangian-by-dietterich-labs-2018" class="multiline"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/IFRyN3fQMO8" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-deriving-the-qed-lagrangian-by-dietterich-labs-2018"><span class="caption-prefix">Video 17. </span></a><div class="title">Deriving the <a href="#quantum-electrodynamics-lagrangian">qED Lagrangian</a> by <a href="particle-physics#dietterich-labs">Dietterich Labs</a> (2018)</div> <a href="https://www.youtube.com/watch?v=IFRyN3fQMO8">Source</a>. <div class="p" id="_176">As mentioned at the start of the video, he starts with the <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a> Lagrangian derived in a previous video. It has nothing to do with <a href="electromagnetism">electromagnetism</a> specifically.</div><div class="p" id="_177">He notes that that <a href="relativistic-quantum-mechanics#dirac-lagrangian">Dirac Lagrangian</a>, besides being globally <a href="relativity#lorentz-invariant">Lorentz invariant</a>, it also also has a global <a href="geometry#unitary-group-of-degree-1"><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mopen">(</span><span class="mord">1</span><span class="mclose">)</span></span></span></span></a> invariance.</div><div class="p" id="_178">However, it does not have a local invariance if the <a href="geometry#unitary-group-of-degree-1"><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mopen">(</span><span class="mord">1</span><span class="mclose">)</span></span></span></span></a> transformation depends on the point in spacetime.</div><div class="p" id="_179">He doesn't mention it, but I think this is highly desirable, because in general <a href="geometry#local-symmetries-of-the-lagrangian-imply-conserved-currents">local symmetries of the Lagrangian imply conserved currents</a>, and in this case we want conservation of charges.</div><div class="p" id="_180">To fix that, he adds an extra <a href="#gauge-field">gauge field</a> <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">μ</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span> (a field of <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">4</span></span></span></span> matrices) to the regular derivative, and the resulting derivative has a fancy name: the <a href="calculus#covariant-derivative">covariant derivative</a>.</div><div class="p" id="_181">Then finally he notes that this <a href="#gauge-field">gauge field</a> he had to add has to transform exactly like the <a href="electromagnetism#electromagnetic-four-potential">electromagnetic four-potential</a>!</div><div class="p" id="_182">So he uses that as the gauge, and also adds in the <a href="relativity#maxwell-lagrangian">Maxwell Lagrangian</a> in the same go. It is kind of a guess, but it is a natural guess, and it turns out to be correct.</div><div class="p" id="_183"><a href="https://www.youtube.com/watch?v=IFRyN3fQMO8&lc=UgzNGkLXdwcSl7z8Lap4AaABAg">www.youtube.com/watch?v=IFRyN3fQMO8&lc=UgzNGkLXdwcSl7z8Lap4AaABAg</a></div></figcaption></figure></div><div class="h" id="what-does-it-mean-that-photons-are-force-carriers-for-electromagnetism"><div class="notnav"><h3><a href="what-does-it-mean-that-photons-are-force-carriers-for-electromagnetism">What does it mean that photons are force carriers for electromagnetism?</a></h3><span class="hover-meta"> <a class="split" href="what-does-it-mean-that-photons-are-force-carriers-for-electromagnetism"></a><span class="metrics"><span class="wcntr"> Words: 254</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics" class="u"> Quantum electrodynamics</a><a href="#_toc/what-does-it-mean-that-photons-are-force-carriers-for-electromagnetism" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/what-does-it-mean-that-photons-are-force-carriers-for-electromagnetism"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_184"><a href="https://physics.stackexchange.com/questions/61095/photon-as-the-carrier-of-the-electromagnetic-force">physics.stackexchange.com/questions/61095/photon-as-the-carrier-of-the-electromagnetic-force</a></div><div class="p" id="_185">TODO find/create decent answer.</div><div class="p" id="_186">I think the best answer is something along:<div class="list"><ul id="_187"><li id="_188"><a href="geometry#local-symmetries-of-the-lagrangian-imply-conserved-currents">local symmetries of the Lagrangian imply conserved currents</a>. <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mopen">(</span><span class="mord">1</span><span class="mclose">)</span></span></span></span> gives conserved charges.</li><li id="_189">OK now. We want a local <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mopen">(</span><span class="mord">1</span><span class="mclose">)</span></span></span></span> symmetry. And we also want:<div class="list"><ul id="_190"><li id="_191"><a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a>: quantum relativistic Newton's laws that specify what forces do to the fields</li><li id="_192"><a href="electromagnetism">electromagnetism</a>: specifies what causes forces based on currents. But not what it does to masses.</li></ul></div>Given all of that, the most obvious and direct thing we reach a guess at the <a href="#quantum-electrodynamics-lagrangian">quantum electrodynamics Lagrangian</a> is <a href="#video-deriving-the-qed-lagrangian-by-dietterich-labs-2018">Video 17. "Deriving the qED Lagrangian by Dietterich Labs (2018)"</a></li></ul></div></div><div class="p" id="_193">A basic non-precise intuition is that a good model of reality is that electrons do not "interact with one another directly via the electromagnetic field".</div><div class="p" id="_194">A better model happens to be the <a href="">quantum field theory</a> view that the electromagnetic field interacts with the photon field but not directly with itself, and then the photon field interacts with parts of the electromagnetic field further away.</div><div class="p" id="_195">The more precise statement is that the <a href="#photon-field">photon field</a> is a gauge field of the electromagnetic force under local U(1) symmetry, which is described by a <a href="geometry#lie-group">Lie group</a>. TODO understand.</div><div class="p" id="_196">This idea was first applied in <a href="relativity#general-relativity">general relativity</a>, where <a href="physicist#albert-einstein">Einstein</a> understood that the "force of <a href="relativity#gravity">gravity</a>" can be understood just in terms of symmetry and curvature of space. This was later applied o <a href="#quantum-electrodynamics">quantum electrodynamics</a> and the entire <a href="standard-model">Standard Model</a>.</div><div class="p" id="_197">From <a href="#video-lorenzo-sadun-on-the-yang-mills-and-mass-gap-millennium-problem">Video 9. "Lorenzo Sadun on the "Yang-Mills and Mass Gap" Millennium problem"</a>:<div class="list"><ul id="_198"><li id="_199"><a href="https://www.youtube.com/watch?v=pCQ9GIqpGBI&t=1663s">www.youtube.com/watch?v=pCQ9GIqpGBI&t=1663s</a> mentions this idea first came about from <a href="physicist#hermann-weyl">Hermann Weyl</a>.</li><li id="_200"><a href="https://youtu.be/pCQ9GIqpGBI?t=2827">youtu.be/pCQ9GIqpGBI?t=2827</a> mentions that in that case the curvature is given by the <a href="electromagnetism#electromagnetic-tensor">electromagnetic tensor</a>.</li></ul></div></div><div class="p" id="_201">Bibliography:<div class="list"><ul id="_202"><li id="_203"><a href="https://www.youtube.com/watch?v=qtf6U3FfDNQ">www.youtube.com/watch?v=qtf6U3FfDNQ</a> Symmetry and Quantum Electrodynamics (The Standard Model Part 1) by ZAP Physics (2021)</li><li id="_204"><a href="https://www.youtube.com/watch?v=OQF7kkWjVWM">www.youtube.com/watch?v=OQF7kkWjVWM</a> The Symmetry and Simplicity of the Laws of Nature and the Higgs Boson by Juan Maldacena (2012). <a href="linguistics#meh">Meh</a>, also too basic.</li></ul></div></div><div class="h" id="photon-field"><div class="notnav"><h3><a href="photon-field">Photon field</a></h3><span class="hover-meta"> <a class="split" href="photon-field"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics" class="u"> Quantum electrodynamics</a><a href="#_toc/photon-field" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/photon-field"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="schwinger-effect"><div class="notnav"><h3><a href="schwinger-effect">Schwinger effect</a></h3><span class="hover-meta"> <a class="split" href="schwinger-effect"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics" class="u"> Quantum electrodynamics</a><a href="#_toc/schwinger-effect" class="toc"></a><a href="https://en.wikipedia.org/wiki/Schwinger_effect" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/schwinger-effect"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="feynman-diagram"><div class="notnav"><h3><a href="feynman-diagram">Feynman diagram</a></h3><span class="hover-meta"> <a class="split" href="feynman-diagram"></a><span class="metrics"><span class="wcntr"> Words: 75</span><span class="dcnt"> Articles: 2</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics" class="u"> Quantum electrodynamics</a><a href="#_toc/feynman-diagram" class="toc"></a><a href="https://en.wikipedia.org/wiki/Feynman_diagram" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/feynman-diagram"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_205">I think they are a tool to calculate the probability of different types of particle decays and particle collision outcomes. TODO Minimal example of that.</div><div class="p" id="_206">And they can be derived from a more complete <a href="#quantum-electrodynamics">quantum electrodynamics</a> formulation via <a href="mathematics#perturbation-theory">perturbation theory</a>.</div><div class="p" id="_207">Can be used for all of <a href="#quantum-electrodynamics">quantum electrodynamics</a>, <a href="#weak-interaction">weak interaction</a> and <a href="#quantum-chromodynamics">quantum chromodynamics</a>.</div><div class="p" id="_208">At <a href="#richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979">Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)</a>, an intuitive explanation of them in termes of sum of products of <a href="#propagator">propagators</a> is given.</div><div class="list"><ul id="_209"><li id="_210"><a href="https://www.youtube.com/watch?v=fG52mXN-uWI">www.youtube.com/watch?v=fG52mXN-uWI</a> The Secrets of Feynman Diagrams | Space Time by <a href="particle-physics#pbs-space-time">PBS Space Time</a> (2017)</li></ul></div><div class="h" id="feynman-diagram-solver"><div class="notnav"><h4><a href="feynman-diagram-solver">Feynman diagram solver</a></h4><span class="hover-meta"> <a class="split" href="feynman-diagram-solver"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#feynman-diagram" class="u"> Feynman diagram</a><a href="#_toc/feynman-diagram-solver" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/feynman-diagram-solver"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_211"><a href="https://physics.stackexchange.com/questions/96510/software-for-calculating-feynman-diagrams">physics.stackexchange.com/questions/96510/software-for-calculating-feynman-diagrams</a></div><div class="h" id="does-the-exact-position-of-vertices-matter-in-feynman-diagrams"><div class="notnav"><h4><a href="does-the-exact-position-of-vertices-matter-in-feynman-diagrams">Does the exact position of vertices matter in Feynman diagrams?</a></h4><span class="hover-meta"> <a class="split" href="does-the-exact-position-of-vertices-matter-in-feynman-diagrams"></a><span class="metrics"><span class="wcntr"> Words: 3</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#feynman-diagram" class="u"> Feynman diagram</a><a href="#_toc/does-the-exact-position-of-vertices-matter-in-feynman-diagrams" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/does-the-exact-position-of-vertices-matter-in-feynman-diagrams"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_212">No, but why?</div><div class="list"><ul id="_213"><li id="_214"><a href="https://physics.stackexchange.com/questions/297004/feynman-diagram-and-uncertainty/297006">physics.stackexchange.com/questions/297004/feynman-diagram-and-uncertainty/297006</a></li></ul></div><div class="h" id="wheeler-feynman-absorber-theory"><div class="notnav"><h3><a href="wheeler-feynman-absorber-theory">Wheeler-Feynman absorber theory</a></h3><span class="hover-meta"> <a class="split" href="wheeler-feynman-absorber-theory"></a><span class="metrics"><span class="wcntr"> Words: 10</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics" class="u"> Quantum electrodynamics</a><a href="#_toc/wheeler-feynman-absorber-theory" class="toc"></a><a href="https://en.wikipedia.org/wiki/Wheeler–Feynman absorber theory" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/wheeler-feynman-absorber-theory"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_215">What they presented on <a href="richard-feynman-s-first-seminar-in-1941">richard Feynman's first seminar in 1941</a>. Does not include <a href="quantum-mechanics">quantum mechanics</a> it seems.</div><div class="h" id="cavity-quantum-electrodynamics"><div class="notnav"><h3><a href="cavity-quantum-electrodynamics">Cavity quantum electrodynamics</a></h3><span class="hover-meta"> <a class="split" href="cavity-quantum-electrodynamics"></a><span class="metrics"><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics" class="u"> Quantum electrodynamics</a><a href="#_toc/cavity-quantum-electrodynamics" class="toc"></a><a href="https://en.wikipedia.org/wiki/Cavity_quantum_electrodynamics" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/cavity-quantum-electrodynamics"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="circuit-quantum-electrodynamics"><div class="notnav"><h4><a href="circuit-quantum-electrodynamics">Circuit quantum electrodynamics</a></h4><span class="hover-meta"> <a class="split" href="circuit-quantum-electrodynamics"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#cavity-quantum-electrodynamics" class="u"> Cavity quantum electrodynamics</a><a href="#_toc/circuit-quantum-electrodynamics" class="toc"></a><a href="https://en.wikipedia.org/wiki/Circuit_quantum_electrodynamics" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/circuit-quantum-electrodynamics"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="positrons-are-electrons-travelling-back-in-time"><div class="notnav"><h3><a href="positrons-are-electrons-travelling-back-in-time">Positrons are electrons travelling back in time</a></h3><span class="hover-meta"> <a class="split" href="positrons-are-electrons-travelling-back-in-time"></a><span class="metrics"><span class="wcntr"> Words: 4</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics" class="u"> Quantum electrodynamics</a><a href="#_toc/positrons-are-electrons-travelling-back-in-time" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/positrons-are-electrons-travelling-back-in-time"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_216">TODO understand this stuff:<div class="list"><ul id="_217"><li id="_218"><a href="https://physics.stackexchange.com/questions/144607/are-all-positrons-electrons-traveling-back-in-time">physics.stackexchange.com/questions/144607/are-all-positrons-electrons-traveling-back-in-time</a></li><li id="_219"><a href="https://www.quora.com/Is-a-positron-just-an-electron-going-backwards-in-time?share=1">www.quora.com/Is-a-positron-just-an-electron-going-backwards-in-time?share=1</a></li></ul></div></div><div class="h" id="quantum-electrodynamics-bibliography"><div class="notnav"><h3><a href="quantum-electrodynamics-bibliography">Quantum electrodynamics bibliography</a></h3><span class="hover-meta"> <a class="split" href="quantum-electrodynamics-bibliography"></a><span class="metrics"><span class="wcntr"> Words: 984</span><span class="dcnt"> Articles: 9</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics" class="u"> Quantum electrodynamics</a><a href="#_toc/quantum-electrodynamics-bibliography" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-electrodynamics-bibliography"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_220"><a href="http://fafnir.phyast.pitt.edu/py3765/">fafnir.phyast.pitt.edu/py3765/</a> Phys3765 Advanced Quantum Mechanics -- QFT-I Fall 2012 by E.S. Swanson mentions several milestone texts including:<div class="list"><ul id="_221"><li id="_222"><a href="#advanced-quantum-mechanics-by-freeman-dyson-1951">Advanced quantum mechanics by Freeman Dyson (1951)</a></li></ul></div></div><div class="h" id="quantum-theory-of-radiation-by-fermi-1932"><div class="notnav"><h4><a href="quantum-theory-of-radiation-by-fermi-1932">Quantum Theory of Radiation by Fermi (1932)</a></h4><span class="hover-meta"> <a class="split" href="quantum-theory-of-radiation-by-fermi-1932"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><a href="#_toc/quantum-theory-of-radiation-by-fermi-1932" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-theory-of-radiation-by-fermi-1932"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="advanced-quantum-mechanics-by-freeman-dyson-1951"><div class="notnav"><h4><a href="advanced-quantum-mechanics-by-freeman-dyson-1951">Advanced quantum mechanics by Freeman Dyson (1951)</a></h4><span class="hover-meta"> <a class="split" href="advanced-quantum-mechanics-by-freeman-dyson-1951"></a><span class="metrics"><span class="wcntr"> Words: 84</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><a href="#_toc/advanced-quantum-mechanics-by-freeman-dyson-1951" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/advanced-quantum-mechanics-by-freeman-dyson-1951"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="physicist#work-by-freeman-dyson">Work by Freeman Dyson</a></span></div></nav></div><div class="p" id="_224"><a href="https://arxiv.org/abs/quant-ph/0608140v1">arxiv.org/abs/quant-ph/0608140v1</a></div><div class="p" id="_225">Lecture notes that were apparently very popular at <a href="university#cornell-university">Cornell University</a>. In this period he was actively synthesizing the revolutionary bullshit <a href="richard-feynman">Richard Feynman</a> and <a href="physicist#julian-schwinger">Julian Schwinger</a> were writing and making it understandable to the more general <a href="physicist">physicist</a> audience, so it might be a good reading.</div><div class="p" id="_226"><div><blockquote id="_227">We shall not develop straightaway a correct theory including many particles. Instead we follow the historical development. We try to make a relativistic quantum theory of one particle, find out how far we can go and where we get into trouble.</blockquote></div>Oh yes, see also: <a href="#dirac-equation-vs-quantum-electrodynamics">Dirac equation vs quantum electrodynamics</a>.</div><div class="h" id="selected-papers-on-quantum-electrodynamics-by-julian-schwinger-1958"><div class="notnav"><h4><a href="selected-papers-on-quantum-electrodynamics-by-julian-schwinger-1958">Selected Papers on Quantum Electrodynamics by Julian Schwinger (1958)</a></h4><span class="hover-meta"> <a class="split" href="selected-papers-on-quantum-electrodynamics-by-julian-schwinger-1958"></a><span class="metrics"><span class="wcntr"> Words: 11</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><a href="#_toc/selected-papers-on-quantum-electrodynamics-by-julian-schwinger-1958" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/selected-papers-on-quantum-electrodynamics-by-julian-schwinger-1958"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_228">Recommended by <a href="stack-overflow#ron-maimon">Ron Maimon</a> at <a href="https://physics.stackexchange.com/questions/18632/good-book-on-the-history-of-quantum-mechanics/18643#18643">physics.stackexchange.com/questions/18632/good-book-on-the-history-of-quantum-mechanics/18643#18643</a>.</div><div class="p" id="_229"><a href="physicist#julian-schwinger">Julian Schwinger</a>'s selection of <a href="education#academic-paper">academic papers</a> by himself and others.</div><div class="h" id="richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979"><div class="notnav"><h4><a href="richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979">Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)</a></h4><span class="hover-meta"> <a class="split" href="richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979"></a><span class="metrics"><span class="wcntr"> Words: 823</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><a href="#_toc/richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="work-by-richard-feynman">Work by Richard Feynman</a></span></div></nav></div><div class="p" id="_231">Talk title shown on intro: "Today's Answers to Newton's Queries about Light".</div><div class="p" id="_232">6 hour lecture, where he tries to explain it to an audience that does not know any modern physics. This is a noble effort.</div><div class="p" id="_233">Part of The Douglas Robb Memorial Lectures lecture series.</div><div class="p" id="_234">Feynman apparently also made a book adaptation: <a href="https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter">QED: The Strange Theory of Light and Matter</a>. That book is basically word by word the same as the presentation, including the diagrams.</div><div class="p" id="_235">According to <a href="http://www.feynman.com/science/qed-lectures-in-new-zealand/">www.feynman.com/science/qed-lectures-in-new-zealand/</a> the official upload is at <a href="http://www.vega.org.uk/video/subseries/8">www.vega.org.uk/video/subseries/8</a> and Vega does show up as a watermark on the video (though it is too pixilated to guess without knowing it), a project that has been discontinued and has has a non-permissive license. Newbs.</div><div class="p" id="_236">4 parts:<div class="list"><ul id="_237"><li id="_238">Part 1: is saying "<a href="photon">photons</a> exist"</li><li id="_239">Part 2: is amazing, and describes how photons move as a sum of all possible paths, not sure if it is relativistic at all though, and suggests that something is minimized in that calculation (the <a href="mechanics#action-physics">action</a>)</li><li id="_240"><div class="p" id="_241">Part 3: is where he hopelessly tries to explain the crucial part of how electrons join the picture in a similar manner to how photons do.</div><div class="p" id="_242">He does make the link to light, saying that there is a function <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span> which gives the amplitude for a photon going from A to B, where A and B are spacetime events.</div><div class="p" id="_243">And then he mentions that there is a similar function <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span> for an electron to go from A to B, but says that that function is too complicated, and gives no intuition unlike the photon one.</div><div class="p" id="_244">He does not mention it, but P and E are the so called <a href="#propagator">propagators</a>.</div><div class="p" id="_245">This is likely the <a href="#path-integral-formulation">path integral formulation</a> of QED.</div><div class="p" id="_246">On <a href="#quantum-mechanical-view-of-reality-by-richard-feynman-1983">Quantum Mechanical View of Reality by Richard Feynman (1983)</a> he mentions that <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span></span></span></span> is a <a href="calculus#bessel-function">Bessel function</a>, without giving further detail.</div><div class="p" id="_247">And also mentions that:<div class="math" id="_248"><div><div class="equation"><div><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">m</span><span class="mclose">)</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span></div><div class="number"><a href="#_248">(2)</a></div></div></div></div>where <code>m</code> is basically a scale factor.<br>such that both are very similar. And that something similar holds for many other particles.</div><div class="p" id="_249">And then, when you draw a <a href="#feynman-diagram">Feynman diagram</a>, e.g. electron emits photon and both are detected at given positions, you sum over all the possibilities, each amplitude is given by:<div class="math" id="_250"><div><div class="equation"><div><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mclose">)</span></span></span></span></div><div class="number"><a href="#_250">(3)</a></div></div></div></div>summed over all possible <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span></span></span></span> <a href="relativity#spacetime">Spacetime</a> points.</div><div class="p" id="_251">This is basically well said at: <a href="https://youtu.be/rZvgGekvHes?t=3349">youtu.be/rZvgGekvHes?t=3349</a> from <a href="#quantum-mechanical-view-of-reality-by-richard-feynman-1983">Quantum Mechanical View of Reality by Richard Feynman (1983)</a>.</div><div class="p" id="_252">TODO: how do electron velocities affect where they are likely to end up? <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mclose">)</span></span></span></span> suggests the probability only depends on the spacetime points.</div><div class="p" id="_253">Also, this clarifies why computations in QED are so insane: you have to sum over every possible point in space!!! TODO but then how do we calculate anything at all in practice?</div></li><li id="_254">Part 4: known problems with QED and thoughts on QCD. Boring.</li></ul></div>This talk has the merit of being very experiment oriented on part 2, big kudos: <a href="physics#how-to-teach-and-learn-physics">how to teach and learn physics</a></div><div class="figure"><figure id="video-richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979-uploaded-by-trev-m-2015" class="multiline"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/Alj6q4Y0TNE" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979-uploaded-by-trev-m-2015"><span class="caption-prefix">Video 18. </span></a><div class="title">Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) uploaded by Trev M (2015)</div> <a href="https://www.youtube.com/watch?v=Alj6q4Y0TNE">Source</a>. Single upload version. Let's use this one for the timestamps I guess.<div class="list"><ul id="_255"><li id="_256"><a href="https://youtu.be/Alj6q4Y0TNE?t=2217">youtu.be/Alj6q4Y0TNE?t=2217</a>: <a href="photon#photomultiplier-tube">photomultiplier tube</a></li><li id="_257"><a href="https://youtu.be/Alj6q4Y0TNE?t=2410">youtu.be/Alj6q4Y0TNE?t=2410</a>: <a href="quantum-mechanics#local-hidden-variable-theory">local hidden-variable theory</a></li><li id="_258"><a href="https://youtu.be/Alj6q4Y0TNE?t=6444">youtu.be/Alj6q4Y0TNE?t=6444</a>: mirror experiment shown at <a href="https://en.wikipedia.org/w/index.php?title=Quantum_electrodynamics&oldid=991301352#Probability_amplitudes">en.wikipedia.org/w/index.php?title=Quantum_electrodynamics&oldid=991301352#Probability_amplitudes</a></li><li id="_259"><a href="https://youtu.be/Alj6q4Y0TNE?t=7309">youtu.be/Alj6q4Y0TNE?t=7309</a>: mirror experiment with a <a href="photon#diffraction-grating">diffraction grating</a> pattern painted black leads to reflection at a weird angle</li><li id="_260"><a href="https://youtu.be/Alj6q4Y0TNE?t=7627">youtu.be/Alj6q4Y0TNE?t=7627</a>: detector under water to explain <a href="calculus#refraction">refraction</a></li><li id="_261"><a href="https://youtu.be/Alj6q4Y0TNE?t=8050">youtu.be/Alj6q4Y0TNE?t=8050</a>: explains <a href="photon#biconvex-spherical-lens">biconvex spherical lens</a> in terms of minimal times</li><li id="_262"><a href="https://youtu.be/Alj6q4Y0TNE?t=8402">youtu.be/Alj6q4Y0TNE?t=8402</a>: mentions that for events in a series, you multiply the complex number of each step</li><li id="_263"><a href="https://youtu.be/Alj6q4Y0TNE?t=9270">youtu.be/Alj6q4Y0TNE?t=9270</a>: mentions that the up to this point, ignored:<div class="list"><ul id="_264"><li id="_265">amplitude shrinks down with distance</li><li id="_266"><a href="photon#photon-polarization">photon polarization</a></li></ul></div>but it should not be too hard to add those</li><li id="_267"><a href="https://youtu.be/Alj6q4Y0TNE?t=11697">youtu.be/Alj6q4Y0TNE?t=11697</a>: finally starts electron interaction. First point is to add time of event detection.</li><li id="_268"><a href="https://youtu.be/Alj6q4Y0TNE?t=13704">youtu.be/Alj6q4Y0TNE?t=13704</a>: electron between plates, and mentions the word <a href="mechanics#action-physics">action</a>, without giving a clear enough idea of what it is unfortunately</li><li id="_269"><a href="https://youtu.be/Alj6q4Y0TNE?t=14467">youtu.be/Alj6q4Y0TNE?t=14467</a>: mentions <a href="standard-model#positron">positrons</a> going back in time, but does not clarify it well enough</li><li id="_270"><a href="https://youtu.be/Alj6q4Y0TNE?t=16614">youtu.be/Alj6q4Y0TNE?t=16614</a>: on the fourth part, half is about frontiers in <a href="#quantum-electrodynamics">quantum electrodynamics</a>, and half full blown <a href="standard-model#theory-of-everything">theory of everything</a>. The QED part goes into <a href="#renormalization">renormalization</a> and the large number of parameters of the <a href="standard-model">Standard Model</a></li></ul></div></figcaption></figure></div><div class="figure"><figure id="video-richard-feynman-lecture-on-quantum-electrodynamics-1-8"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/LPDP_8X5Hug" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-richard-feynman-lecture-on-quantum-electrodynamics-1-8"><span class="caption-prefix">Video 19. </span></a><div class="title">Richard Feynman Lecture on Quantum Electrodynamics 1/8</div>. <a href="https://www.youtube.com/watch?v=LPDP_8X5Hug">Source</a>. </figcaption></figure></div><div class="h" id="quantum-mechanical-view-of-reality-by-richard-feynman-1983"><div class="notnav"><h5><a href="quantum-mechanical-view-of-reality-by-richard-feynman-1983">Quantum Mechanical View of Reality by Richard Feynman (1983)</a></h5><span class="hover-meta"> <a class="split" href="quantum-mechanical-view-of-reality-by-richard-feynman-1983"></a><span class="metrics"><span class="wcntr"> Words: 176</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979" class="u"> Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)</a><a href="#_toc/quantum-mechanical-view-of-reality-by-richard-feynman-1983" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-mechanical-view-of-reality-by-richard-feynman-1983"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_271">Sample playlist: <a href="https://www.youtube.com/playlist?list=PLW_HsOU6YZRkdhFFznHNEfua9NK3deBQy">www.youtube.com/playlist?list=PLW_HsOU6YZRkdhFFznHNEfua9NK3deBQy</a></div><div class="p" id="_272">Basically the same content as: <a href="#richard-feynman-quantum-electrodynamics-lecture-at-university-of-auckland-1979">Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)</a>, but maybe there is some merit to this talk, as it is a bit more direct in some points. This is consistent with what is mentioned at <a href="http://www.feynman.com/science/qed-lectures-in-new-zealand/">www.feynman.com/science/qed-lectures-in-new-zealand/</a> that the Auckland lecture was the first attempt.</div><div class="p" id="_273">Some more information at: <a href="https://iucat.iu.edu/iub/5327621">iucat.iu.edu/iub/5327621</a></div><div class="p" id="_274">By Mill Valley, CA based producer "Sound Photosynthesis", some info on their website: <a href="http://sound.photosynthesis.com/Richard_Feynman.html">sound.photosynthesis.com/Richard_Feynman.html</a></div><div class="p" id="_275">They are mostly a <a href="religion#new-age">New Age</a> production company it seems, which highlights Feynman's absolute cult status. E.g. on the last video, he's not wearing shoes, like a proper guru.</div><div class="p" id="_276">Feynman liked to meet all kinds of weird people, and at some point he got interested in the <a href="religion#new-age">New Age</a> <a href="religion#esalen-institute">Esalen Institute</a>. <a href="surely-you-re-joking-mr-feynman">Surely You're Joking, Mr. Feynman</a> this kind of experience a bit, there was nude bathing on a pool that oversaw the sea, and a guy offered to give a massage to the he nude girl and the accepted.</div><div class="p" id="_277"><a href="https://youtu.be/rZvgGekvHest=5105">youtu.be/rZvgGekvHest=5105</a> actually talks about <a href="relativistic-quantum-mechanics#spin-physics">spin</a>, notably that the endpoint events also have a spin, and that the transition rules take spin into account by rotating thing, and that the transition rules take spin into account by rotating things.</div><div class="h" id="quantum-electrodynamics-by-lifshitz-et-al-2nd-edition-1982"><div class="notnav"><h4><a href="quantum-electrodynamics-by-lifshitz-et-al-2nd-edition-1982">Quantum electrodynamics by Lifshitz et al. 2nd edition (1982)</a></h4><span class="hover-meta"> <a class="split" href="quantum-electrodynamics-by-lifshitz-et-al-2nd-edition-1982"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><a href="#_toc/quantum-electrodynamics-by-lifshitz-et-al-2nd-edition-1982" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-electrodynamics-by-lifshitz-et-al-2nd-edition-1982"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="physics-253a-by-sidney-coleman-1986"><div class="notnav"><h4><a href="physics-253a-by-sidney-coleman-1986">Physics 253a by Sidney Coleman (1986)</a></h4><span class="hover-meta"> <a class="split" href="physics-253a-by-sidney-coleman-1986"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><a href="#_toc/physics-253a-by-sidney-coleman-1986" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/physics-253a-by-sidney-coleman-1986"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="qed-and-the-men-who-made-it-dyson-feynman-schwinger-and-tomonaga-by-silvan-schweber-1994"><div class="notnav"><h4><a href="qed-and-the-men-who-made-it-dyson-feynman-schwinger-and-tomonaga-by-silvan-schweber-1994">QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994)</a></h4><span class="hover-meta"> <a class="split" href="qed-and-the-men-who-made-it-dyson-feynman-schwinger-and-tomonaga-by-silvan-schweber-1994"></a><span class="metrics"><span class="wcntr"> Words: 48</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><a href="#_toc/qed-and-the-men-who-made-it-dyson-feynman-schwinger-and-tomonaga-by-silvan-schweber-1994" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/qed-and-the-men-who-made-it-dyson-feynman-schwinger-and-tomonaga-by-silvan-schweber-1994"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_278">Available for <a href="economy#free">free</a> <a href="computer#internet">online</a> <a href="economy#renting">rent</a> on the <a href="website#internet-archive">Internet Archive</a>: <a href="https://archive.org/details/qedmenwhomadeitd0000schw">archive.org/details/qedmenwhomadeitd0000schw</a></div><div class="p" id="_279">This book has formulas on it, which is quite cool!! And the formulas are basically not understandable unless you know the subject pretty well already in advance. It is however possible to skip over them and get back to the little personal stories.</div><div class="h" id="advanced-quantum-mechanics-ii-by-douglas-gingrich-2004"><div class="notnav"><h4><a href="advanced-quantum-mechanics-ii-by-douglas-gingrich-2004">Advanced quantum mechanics II by Douglas Gingrich (2004)</a></h4><span class="hover-meta"> <a class="split" href="advanced-quantum-mechanics-ii-by-douglas-gingrich-2004"></a><span class="metrics"><span class="wcntr"> Words: 2</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-electrodynamics-bibliography" class="u"> Quantum electrodynamics bibliography</a><a href="#_toc/advanced-quantum-mechanics-ii-by-douglas-gingrich-2004" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/advanced-quantum-mechanics-ii-by-douglas-gingrich-2004"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_280"><a href="https://sites.ualberta.ca/~gingrich/courses/phys512/phys512.html">sites.ualberta.ca/~gingrich/courses/phys512/phys512.html</a></div><div class="p" id="_281">From <a href="university#university-of-alberta">University of Alberta</a>.</div><div class="h" id="weak-interaction"><div class="notnav"><h2><a href="weak-interaction">Weak interaction</a></h2><span class="hover-meta"> <a class="split" href="weak-interaction"></a><span class="metrics"><span class="wcntr"> Words: 271</span><span class="dcnt"> Articles: 9</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="" class="u"> Quantum field theory</a><a href="#_toc/weak-interaction" class="toc"></a><a href="https://en.wikipedia.org/wiki/Weak_interaction" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/weak-interaction"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_282">Explains <a href="particle-physics#beta-decay">beta decay</a>. TODO why/how.</div><div class="p" id="_283">Maybe a good view of why this force was needed given <a href="particle-physics#beta-decay">beta decay</a> experiments is: in beta decay, a <a href="standard-model#neutron">neutron</a> is getting split up into an <a href="standard-model#electron">electron</a> and a <a href="standard-model#proton">proton</a>. Therefore, those charges must be contained inside the neutron somehow to start with. But then what could possibly make a positive and a negative particle separate?<div class="list"><ul id="_284"><li id="_285">the <a href="electromagnetism">electromagnetic force</a> should hold them together</li><li id="_286">the <a href="#strong-interaction">strong force</a> seems to hold positive charges together. Could it then be pushing opposite-charges apart? Why not?</li><li id="_287"><a href="relativity#gravity">gravity</a> is too weak</li></ul></div></div><div class="p" id="_288"><a href="http://www.thestargarden.co.uk/Weak-nuclear-force.html">www.thestargarden.co.uk/Weak-nuclear-force.html</a> gives a quick and dirty:<div><blockquote id="_289">Beta decay could not be explained by the strong nuclear force, the force that's responsible for holding the atomic nucleus together, because this force doesn't affect electrons. It couldn't be explained by the electromagnetic force, because this does not affect <a href="standard-model#neutron">neutrons</a>, and the force of <a href="relativity#gravity">gravity</a> is far too weak to be responsible. Since this new atomic force was not as strong as the strong nuclear force, it was dubbed the weak nuclear force.</blockquote></div>Also interesting:<div><blockquote id="_290">While the photon 'carries' charge, and therefore mediates the <a href="electromagnetism">electromagnetic force</a>, the <a href="#z-boson">Z</a> and <a href="#w-boson">W</a> <a href="relativistic-quantum-mechanics#boson">bosons</a> are said to carry a property known as 'weak isospin'. <a href="#w-boson">W bosons</a> mediate the weak force when particles with charge are involved, and <a href="#z-boson">Z bosons</a> mediate the weak force when neutral particles are involved.</blockquote></div></div><div class="figure"><figure id="video-weak-nuclear-force-and-standard-model-of-particle-physics-by-physics-videos-by-eugene-khutoryansky-2018"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/iIWTRwJlrGo" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-weak-nuclear-force-and-standard-model-of-particle-physics-by-physics-videos-by-eugene-khutoryansky-2018"><span class="caption-prefix">Video 20. </span></a><div class="title">Weak Nuclear Force and <a href="standard-model">Standard Model</a> of <a href="particle-physics">particle physics</a> by <a href="particle-physics#physics-videos-by-eugene-khutoryansky">Physics Videos by Eugene Khutoryansky</a> (2018)</div> <a href="https://www.youtube.com/watch?v=iIWTRwJlrGo">Source</a>. Some decent visualizations of the field lines.</figcaption></figure></div><div class="h" id="electroweak-interaction"><div class="notnav"><h3><a href="electroweak-interaction">Electroweak interaction</a></h3><span class="hover-meta"> <a class="split" href="electroweak-interaction"></a><span class="metrics"><span class="wcntr"> Words: 15</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#weak-interaction" class="u"> Weak interaction</a><a href="#_toc/electroweak-interaction" class="toc"></a><a href="https://en.wikipedia.org/wiki/Electroweak_interaction" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/electroweak-interaction"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="figure"><figure id="video-electroweak-theory-and-the-origin-of-the-fundamental-forces-by-pbs-space-time-2020"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/qKVpknSKgE0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-electroweak-theory-and-the-origin-of-the-fundamental-forces-by-pbs-space-time-2020"><span class="caption-prefix">Video 21. </span></a><div class="title">Electroweak Theory and the Origin of the Fundamental Forces by <a href="particle-physics#pbs-space-time">PBS Space Time</a> (2020)</div> <a href="https://www.youtube.com/watch?v=qKVpknSKgE0">Source</a>. <a href="ciro-santilli#the-missing-link-between-basic-and-advanced">Unsatisfactory</a>, as usual.</figcaption></figure></div><div class="h" id="parity-violation"><div class="notnav"><h3><a href="parity-violation">Parity violation</a></h3><span class="hover-meta"> <a class="split" href="parity-violation"></a><span class="metrics"><span class="wcntr"> Words: 38</span><span class="dcnt"> Articles: 4</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#weak-interaction" class="u"> Weak interaction</a><a href="#_toc/parity-violation" class="toc"></a><a href="https://en.wikipedia.org/wiki/Parity_violation" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/parity-violation"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_291">This is quite <a href="brain#mind-blown">mind blowing</a>. The <a href="physics#law-of-physics">laws of physics</a> actually differentiate between particles and <a href="relativistic-quantum-mechanics#antimatter">antiparticles</a> moving in opposite directions!!!</div><div class="p" id="_292">Only the <a href="#weak-interaction">weak interaction</a> however does it of the <a href="standard-model#fundamental-interaction">fundamental interactions</a>.</div><div class="p" id="_293">Some historical remarks on <a href="surely-you-re-joking-mr-feynman">Surely You're Joking, Mr. Feynman</a> section "The 7 Percent Solution".</div><div class="p" id="_294">It gets worse of course with <a href="#cp-violation">cP Violation</a>.</div><div class="h" id="wu-experiment"><div class="notnav"><h4><a href="wu-experiment">Wu experiment <span class="meta">(1956)</span></a></h4><span class="hover-meta"> <a class="split" href="wu-experiment"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#parity-violation" class="u"> Parity violation</a><a href="#_toc/wu-experiment" class="toc"></a><a href="https://en.wikipedia.org/wiki/Wu_experiment" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/wu-experiment"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="cp-violation"><div class="notnav"><h4><a href="cp-violation">CP Violation</a></h4><span class="hover-meta"> <a class="split" href="cp-violation"></a><span class="metrics"><span class="dcnt"> Articles: 2</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#parity-violation" class="u"> Parity violation</a><a href="#_toc/cp-violation" class="toc"></a><a href="https://en.wikipedia.org/wiki/CP_Violation" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/cp-violation"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="cpt-symmetry"><div class="notnav"><h5><a href="cpt-symmetry">CPT symmetry</a></h5><span class="hover-meta"> <a class="split" href="cpt-symmetry"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#cp-violation" class="u"> CP Violation</a><a href="#_toc/cpt-symmetry" class="toc"></a><a href="https://en.wikipedia.org/wiki/CPT_symmetry" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/cpt-symmetry"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="strong-cp-problem"><div class="notnav"><h5><a href="strong-cp-problem">Strong CP problem</a></h5><span class="hover-meta"> <a class="split" href="strong-cp-problem"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#cp-violation" class="u"> CP Violation</a><a href="#_toc/strong-cp-problem" class="toc"></a><a href="https://en.wikipedia.org/wiki/Strong_CP_problem" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/strong-cp-problem"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="physics#unsolved-physics-problem">Unsolved physics problem</a></span></div></nav></div><div class="h" id="weak-charge"><div class="notnav"><h3><a href="weak-charge">Weak charge</a></h3><span class="hover-meta"> <a class="split" href="weak-charge"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#weak-interaction" class="u"> Weak interaction</a><a href="#_toc/weak-charge" class="toc"></a><a href="https://en.wikipedia.org/wiki/Weak_charge" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/weak-charge"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="w-boson"><div class="notnav"><h3><a href="w-boson">W boson</a></h3><span class="hover-meta"> <a class="split" href="w-boson"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#weak-interaction" class="u"> Weak interaction</a><a href="#_toc/w-boson" class="toc"></a><a href="https://en.wikipedia.org/wiki/W_boson" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/w-boson"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="standard-model#elementary-particle">Elementary particle</a></span></div></nav></div><div class="h" id="z-boson"><div class="notnav"><h3><a href="z-boson">Z boson</a></h3><span class="hover-meta"> <a class="split" href="z-boson"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#weak-interaction" class="u"> Weak interaction</a><a href="#_toc/z-boson" class="toc"></a><a href="https://en.wikipedia.org/wiki/Z_boson" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/z-boson"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="standard-model#elementary-particle">Elementary particle</a></span></div></nav></div><div class="h" id="quantum-chromodynamics"><div class="notnav"><h2><a href="quantum-chromodynamics">Quantum chromodynamics <span class="meta">(QCD)</span></a></h2><span class="hover-meta"> <a class="split" href="quantum-chromodynamics"></a><span class="metrics"><span class="wcntr"> Words: 123</span><span class="dcnt"> Articles: 11</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="" class="u"> Quantum field theory</a><a href="#_toc/quantum-chromodynamics" class="toc"></a><a href="https://en.wikipedia.org/wiki/Quantum_chromodynamics" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/quantum-chromodynamics"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_300">Formulated as a <a href="">quantum field theory</a>.</div><div class="figure"><figure id="video-quarks-gluon-flux-tubes-strong-nuclear-force-and-quantum-chromodynamics-by-physics-videos-by-eugene-khutoryansky-2018"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/FoR3hq5b5yE" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-quarks-gluon-flux-tubes-strong-nuclear-force-and-quantum-chromodynamics-by-physics-videos-by-eugene-khutoryansky-2018"><span class="caption-prefix">Video 22. </span></a><div class="title">Quarks, Gluon flux tubes, Strong Nuclear Force, & Quantum Chromodynamics by <a href="particle-physics#physics-videos-by-eugene-khutoryansky">Physics Videos by Eugene Khutoryansky</a> (2018)</div> <a href="http://youtube.com/watch?v=FoR3hq5b5yE">Source</a>. Some decent visualizations of how the field lines don't expand out like they do in <a href="electromagnetism">electromagnetism</a>, suggesting <a href="#color-confinement">color confinement</a>.</figcaption></figure></div><div class="figure"><figure id="video-phys-485-lecture-6-feynman-diagrams-by-roger-moore-2016"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/LqUgzxJ8Jss" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-phys-485-lecture-6-feynman-diagrams-by-roger-moore-2016"><span class="caption-prefix">Video 23. </span></a><div class="title">PHYS 485 Lecture 6: Feynman Diagrams by <a href="particle-physics#2011-phys-485-lecture-videos-by-roger-moore-from-the-university-of-alberta">Roger Moore</a> (2016)</div> <a href="https://www.youtube.com/watch?v=LqUgzxJ8Jss">Source</a>. Despite the title, this is mostly about QCD.</figcaption></figure></div><div class="h" id="quark"><div class="notnav"><h3><a href="quark">Quark</a></h3><span class="hover-meta"> <a class="split" href="quark"></a><span class="metrics"><span class="wcntr"> Words: 3</span><span class="dcnt"> Articles: 3</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-chromodynamics" class="u"> Quantum chromodynamics</a><a href="#_toc/quark" class="toc"></a><a href="https://en.wikipedia.org/wiki/Quark" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/quark"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_301">TODO experimental discovery.</div><div class="h" id="down-quark"><div class="notnav"><h4><a href="down-quark">Down quark</a></h4><span class="hover-meta"> <a class="split" href="down-quark"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quark" class="u"> Quark</a><a href="#_toc/down-quark" class="toc"></a><a href="https://en.wikipedia.org/wiki/Down_quark" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/down-quark"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="up-quark"><div class="notnav"><h4><a href="up-quark">Up quark</a></h4><span class="hover-meta"> <a class="split" href="up-quark"></a><span class="metrics"><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quark" class="u"> Quark</a><a href="#_toc/up-quark" class="toc"></a><a href="https://en.wikipedia.org/wiki/Up_quark" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/up-quark"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="why-do-the-up-ad-down-quarks-have-different-masses"><div class="notnav"><h5><a href="why-do-the-up-ad-down-quarks-have-different-masses">Why do the up ad down quarks have different masses?</a></h5><span class="hover-meta"> <a class="split" href="why-do-the-up-ad-down-quarks-have-different-masses"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#up-quark" class="u"> Up quark</a><a href="#_toc/why-do-the-up-ad-down-quarks-have-different-masses" class="toc"></a><a href="https://en.wikipedia.org/wiki/Why_do_the_up_ad_down_quarks_have_different_masses?" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/why-do-the-up-ad-down-quarks-have-different-masses"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_302"><a href="https://www.quora.com/Why-do-up-quarks-and-down-quarks-have-different-charges">www.quora.com/Why-do-up-quarks-and-down-quarks-have-different-charges</a></div><div class="h" id="strange-quark"><div class="notnav"><h3><a href="strange-quark">Strange quark</a></h3><span class="hover-meta"> <a class="split" href="strange-quark"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-chromodynamics" class="u"> Quantum chromodynamics</a><a href="#_toc/strange-quark" class="toc"></a><a href="https://en.wikipedia.org/wiki/Strange_quark" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/strange-quark"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="gluon"><div class="notnav"><h3><a href="gluon">Gluon</a></h3><span class="hover-meta"> <a class="split" href="gluon"></a><span class="metrics"><span class="wcntr"> Words: 21</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-chromodynamics" class="u"> Quantum chromodynamics</a><a href="#_toc/gluon" class="toc"></a><a href="https://en.wikipedia.org/wiki/Gluon" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/gluon"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_303">Force carrier of <a href="#quantum-chromodynamics">quantum chromodynamics</a>, like the <a href="photon">photon</a> is the force carrier of <a href="#quantum-electrodynamics">quantum electrodynamics</a>.</div><div class="p" id="_304">One big difference is that it carrier itself <a href="#color-charge">color charge</a>.</div><div class="h" id="glueball"><div class="notnav"><h4><a href="glueball">Glueball</a></h4><span class="hover-meta"> <a class="split" href="glueball"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#gluon" class="u"> Gluon</a><a href="#_toc/glueball" class="toc"></a><a href="https://en.wikipedia.org/wiki/Glueball" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/glueball"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="proton-decay"><div class="notnav"><h3><a href="proton-decay">Proton decay</a></h3><span class="hover-meta"> <a class="split" href="proton-decay"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-chromodynamics" class="u"> Quantum chromodynamics</a><a href="#_toc/proton-decay" class="toc"></a><a href="https://en.wikipedia.org/wiki/Proton_decay" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/proton-decay"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="strong-interaction"><div class="notnav"><h3><a href="strong-interaction">Strong interaction</a></h3><span class="hover-meta"> <a class="split" href="strong-interaction"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-chromodynamics" class="u"> Quantum chromodynamics</a><a href="#_toc/strong-interaction" class="toc"></a><a href="https://en.wikipedia.org/wiki/Strong_interaction" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/strong-interaction"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="color-charge"><div class="notnav"><h3><a href="color-charge">Color charge</a></h3><span class="hover-meta"> <a class="split" href="color-charge"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-chromodynamics" class="u"> Quantum chromodynamics</a><a href="#_toc/color-charge" class="toc"></a><a href="https://en.wikipedia.org/wiki/Color_charge" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/color-charge"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="color-confinement"><div class="notnav"><h3><a href="color-confinement">Color confinement</a></h3><span class="hover-meta"> <a class="split" href="color-confinement"></a><span class="metrics"><span class="wcntr"> Words: 47</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-chromodynamics" class="u"> Quantum chromodynamics</a><a href="#_toc/color-confinement" class="toc"></a><a href="https://en.wikipedia.org/wiki/Color_confinement" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/color-confinement"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_305">Can be thought as being produced from <a href="#gluon">gluon</a>-gluon lines of the <a href="#feynman-diagram">Feynman diagrams</a> of <a href="#quantum-chromodynamics">quantum chromodynamics</a>. This is in contrast to <a href="#quantum-electrodynamics">quantum electrodynamics</a>, in which there are no <a href="photon">photon</a>-photon vertices, because the photon does not have charge unlike gluons.</div><div class="p" id="_306">This phenomena makes the strong force be very very different from electromagnetism.</div><div class="h" id="quantum-field-theory-simulations"><div class="notnav"><h2><a href="quantum-field-theory-simulations">Quantum field theory simulations</a></h2><span class="hover-meta"> <a class="split" href="quantum-field-theory-simulations"></a><span class="metrics"><span class="wcntr"> Words: 109</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="" class="u"> Quantum field theory</a><a href="#_toc/quantum-field-theory-simulations" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-simulations"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_307">TODO why is it so hard to find anything non perturbative :-(</div><div class="list"><ul id="_308"><li id="_309"><a href="https://www.youtube.com/channel/UCPHFUHiwbpMqC8ONxEICCiQ">www.youtube.com/channel/UCPHFUHiwbpMqC8ONxEICCiQ</a> NanoNebula using raw <a href="programming-language#perl-programming-language">Perl</a> PDFL <a href="https://en.wikipedia.org/wiki/Perl_Data_Language">en.wikipedia.org/wiki/Perl_Data_Language</a> (the Perl <a href="programming-language#numpy">NumPy</a>)</li><li id="_310"><a href="https://www.youtube.com/watch?v=9TJe1Pr5c9Q">www.youtube.com/watch?v=9TJe1Pr5c9Q</a> "Interplay of Quantum Electrodynamics and Quantum Chromodynamics in the Nontrivial Vacuum" by CSSM Visualisation (2019)</li></ul></div><div class="p" id="_311">On a <a href="quantum-computing">quantum computer</a>...:<div class="list"><ul id="_312"><li id="_313"><a href="https://www.cornell.edu/video/john-preskill-simulating-quantum-field-theory-with-quantum-computer">www.cornell.edu/video/john-preskill-simulating-quantum-field-theory-with-quantum-computer</a> Simulating Quantum Field Theory with a Quantum Computer by John Preskill (2019)</li><li id="_314"><a href="https://www.youtube.com/watch?v=Lln-C21u0U8">www.youtube.com/watch?v=Lln-C21u0U8</a> Quantum Simulation from Quantum Chemistry to Quantum Field Theory by Peter Love (2019)</li></ul></div></div><div class="figure"><figure id="video-are-we-living-in-the-matrix-by-david-tong-2020"><div class="float-wrap"><iframe width="560" height="315" loading="lazy" src="https://www.youtube.com/embed/QPMn7SuiHP8" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div><figcaption><a href="#video-are-we-living-in-the-matrix-by-david-tong-2020"><span class="caption-prefix">Video 24. </span></a><div class="title">Are we living in <a href="film#the-matrix-1999">the matrix</a>? by <a href="physicist#david-tong">David Tong</a> (2020)</div> <a href="https://www.youtube.com/watch?v=QPMn7SuiHP8">Source</a>. Talks about how the <a href="#nielsen-ninomiya-theorem">Nielsen-Ninomiya theorem</a> means it is impossible to simulate <a href="">QFT</a> on a computer in the case of a <a href="#lattice-gauge-theory">lattice gauge theory</a>.</figcaption></figure></div><div class="h" id="nielsen-ninomiya-theorem"><div class="notnav"><h3><a href="nielsen-ninomiya-theorem">Nielsen-Ninomiya theorem</a></h3><span class="hover-meta"> <a class="split" href="nielsen-ninomiya-theorem"></a><span class="metrics"><span class="wcntr"> Words: 19</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-simulations" class="u"> Quantum field theory simulations</a><a href="#_toc/nielsen-ninomiya-theorem" class="toc"></a><a href="https://en.wikipedia.org/wiki/Nielsen–Ninomiya_theorem" class="wiki"></a><a href="https://ourbigbook.com/cirosantilli/nielsen-ninomiya-theorem"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="quantum-mechanics#no-go-theorem">No-go theorem</a></span></div></nav></div><div class="p" id="_316">As mentioned at <a href="#video-are-we-living-in-the-matrix-by-david-tong-2020">Video 24. "Are we living in the matrix? by David Tong (2020)"</a> somehow implies that it is difficult or impossible to simulate physics on a computer. Big news!!!</div><div class="h" id="infinities-in-quantum-field-theory"><div class="notnav"><h2><a href="infinities-in-quantum-field-theory">Infinities in quantum field theory</a></h2><span class="hover-meta"> <a class="split" href="infinities-in-quantum-field-theory"></a><span class="metrics"><span class="wcntr"> Words: 13</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="" class="u"> Quantum field theory</a><a href="#_toc/infinities-in-quantum-field-theory" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/infinities-in-quantum-field-theory"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_317">TODO concrete example, please...<div class="list"><ul id="_318"><li id="_319"><a href="https://physics.stackexchange.com/questions/310496/what-is-the-infinity-that-strikes-quantum-field-theory">physics.stackexchange.com/questions/310496/what-is-the-infinity-that-strikes-quantum-field-theory</a></li><li id="_320"><a href="#qed-and-the-men-who-made-it-dyson-feynman-schwinger-and-tomonaga-by-silvan-schweber-1994">QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994)</a> chapter 2.5 "The Divergences" contains a specific example by <a href="physicist#pascual-jordan">Pascual Jordan</a></li></ul></div></div><div class="h" id="mathematical-consistency-of-quantum-field-theory"><div class="notnav"><h3><a href="mathematical-consistency-of-quantum-field-theory">Mathematical consistency of quantum field theory</a></h3><span class="hover-meta"> <a class="split" href="mathematical-consistency-of-quantum-field-theory"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#infinities-in-quantum-field-theory" class="u"> Infinities in quantum field theory</a><a href="#_toc/mathematical-consistency-of-quantum-field-theory" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/mathematical-consistency-of-quantum-field-theory"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_321"><a href="https://physics.stackexchange.com/questions/16142/is-qft-mathematically-self-consistent">physics.stackexchange.com/questions/16142/is-qft-mathematically-self-consistent</a></div><div class="h" id="internal-and-spacetime-symmetries"><div class="notnav"><h2><a href="internal-and-spacetime-symmetries">Internal and spacetime symmetries</a></h2><span class="hover-meta"> <a class="split" href="internal-and-spacetime-symmetries"></a><span class="metrics"><span class="wcntr"> Words: 126</span><span class="dcnt"> Articles: 2</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="" class="u"> Quantum field theory</a><a href="#_toc/internal-and-spacetime-symmetries" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/internal-and-spacetime-symmetries"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_322"><a href="https://physics.stackexchange.com/questions/106392/internal-and-spacetime-symmetries">physics.stackexchange.com/questions/106392/internal-and-spacetime-symmetries</a></div><div class="p" id="_323">The different only shows up for <a href="physics#field-physics">field</a>, not with particles. For fields, there are two types of changes that we can make that can keep the <a href="mechanics#lagrangian">Lagrangian</a> unchanged as mentioned at <a href="physicist#physics-from-symmetry-by-jakob-schwichtenberg-2015">Physics from Symmetry by Jakob Schwichtenberg (2015)</a> chapter "4.5.2 Noether's Theorem for Field Theories - Spacetime":<div class="list"><ul id="_324"><li id="_325"><a href="#spacetime-symmetry">spacetime symmetry</a>: act with the <a href="geometry#poincare-group">Poincaré group</a> on the <a href="relativity#four-vector">Four-vector</a> spacetime inputs of the field itself, i.e. transforming <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mopen">(</span><span class="mord">Φ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord">Φ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span> into <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0019em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mopen">(</span><span class="mord"><span class="mord">Φ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord"><span class="mord">Φ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></li><li id="_326"><a href="#internal-symmetry">internal symmetry</a>: act on the output of the field, i.e.: <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mopen">(</span><span class="mord">Φ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="mord">Φ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mopen">(</span><span class="mord">Φ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="mord">Φ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">))</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></li></ul></div></div><div class="p" id="_327">From <a href="standard-model#defining-properties-of-elementary-particles">defining properties of elementary particles</a>:<div class="list"><ul id="_328"><li id="_329">spacetime:<div class="list"><ul id="_330"><li id="_331"><a href="mechanics#mass">mass</a></li><li id="_332"><a href="relativistic-quantum-mechanics#spin-physics">spin</a></li></ul></div></li><li id="_333">internal<div class="list"><ul id="_334"><li id="_335"><a href="electromagnetism#electric-charge">electric charge</a></li><li id="_336"><a href="#weak-charge">Weak charge</a></li><li id="_337"><a href="#color-charge">color charge</a></li></ul></div></li></ul></div></div><div class="p" id="_338">From the spacetime theory alone, we can derive the <a href="mechanics#lagrangian">Lagrangian</a> for the free theories for each <a href="relativistic-quantum-mechanics#spin-physics">spin</a>:<div class="list"><ul id="_339"><li id="_340"><a href="relativistic-quantum-mechanics#spin-0">spin 0</a>: <a href="relativistic-quantum-mechanics#klein-gordon-equation">Klein-Gordon equation</a></li><li id="_341"><a href="relativistic-quantum-mechanics#spin-half">spin half</a>: <a href="relativistic-quantum-mechanics#dirac-equation">Dirac equation</a></li><li id="_342"><a href="relativistic-quantum-mechanics#spin-1">spin 1</a>: <a href="relativistic-quantum-mechanics#proca-equation">Proca equation</a></li></ul></div>Then the internal symmetries are what add the interaction part of the <a href="mechanics#lagrangian">Lagrangian</a>, which then completes the <a href="standard-model#standard-model-lagrangian">Standard Model Lagrangian</a>.</div><div class="h" id="internal-symmetry"><div class="notnav"><h3><a href="internal-symmetry">Internal symmetry</a></h3><span class="hover-meta"> <a class="split" href="internal-symmetry"></a><span class="metrics"><span class="wcntr"> Words: 2</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#internal-and-spacetime-symmetries" class="u"> Internal and spacetime symmetries</a><a href="#_toc/internal-symmetry" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/internal-symmetry"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_343">See: <a href="#internal-and-spacetime-symmetries">internal and spacetime symmetries</a>.</div><div class="h" id="spacetime-symmetry"><div class="notnav"><h3><a href="spacetime-symmetry">Spacetime symmetry</a></h3><span class="hover-meta"> <a class="split" href="spacetime-symmetry"></a><span class="metrics"><span class="wcntr"> Words: 2</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#internal-and-spacetime-symmetries" class="u"> Internal and spacetime symmetries</a><a href="#_toc/spacetime-symmetry" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/spacetime-symmetry"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_344">See: <a href="#internal-and-spacetime-symmetries">internal and spacetime symmetries</a>.</div><div class="h" id="quantum-field-theory-bibliography"><div class="notnav"><h2><a href="quantum-field-theory-bibliography">Quantum field theory bibliography</a></h2><span class="hover-meta"> <a class="split" href="quantum-field-theory-bibliography"></a><span class="metrics"><span class="wcntr"> Words: 1k</span><span class="dcnt"> Articles: 30</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="" class="u"> Quantum field theory</a><a href="#_toc/quantum-field-theory-bibliography" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-bibliography"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_345"><a href="ciro-santilli">Ciro Santilli</a>'s favorites so far:<div class="list"><ul id="_346"><li id="_347"><a href="physicist#physics-from-symmetry-by-jakob-schwichtenberg-2015">Physics from Symmetry by Jakob Schwichtenberg (2015)</a></li></ul></div></div><div class="p" id="_348">Bibliography of the biliograpy:<div class="list"><ul id="_349"><li id="_350"><a href="https://physics.stackexchange.com/questions/8441/what-is-a-complete-book-for-introductory-quantum-field-theory">physics.stackexchange.com/questions/8441/what-is-a-complete-book-for-introductory-quantum-field-theory</a> "What is a complete book for introductory quantum field theory?"</li><li id="_351"><a href="https://www.quora.com/What-is-the-best-book-to-learn-quantum-field-theory-on-your-own">www.quora.com/What-is-the-best-book-to-learn-quantum-field-theory-on-your-own</a> on <a href="website#quora">Quora</a></li><li id="_352"><a href="https://www.amazon.co.uk/Lectures-Quantum-Field-Theory-Ashok-ebook/dp/B07CL8Y3KY">www.amazon.co.uk/Lectures-Quantum-Field-Theory-Ashok-ebook/dp/B07CL8Y3KY</a></li></ul></div></div><div class="p" id="_353">Recommendations by friend P. C.:<div class="list"><ul id="_354"><li id="_355">The Global Approach to Quantum Field Theory</li><li id="_356">Lecture Notes | Geometry and Quantum Field Theory | Mathematics <a href="https://ocw.mit.edu/courses/mathematics/18-238-geometry-and-quantum-field-theory-fall-2002/lecture-notes/">ocw.mit.edu/courses/mathematics/18-238-geometry-and-quantum-field-theory-fall-2002/lecture-notes/</a></li><li id="_357">Towards the mathematics of quantum field theory (Frederic Paugam)</li><li id="_358">Path Integrals in Quantum Mechanics (J. Zinn–Justin)</li><li id="_359">(B.Hall) Quantum Theory for Mathematicians (B.Hall)</li><li id="_360">Quantum Field Theory and the Standard Model (Schwartz)</li><li id="_361">The Algebra of Grand Unified Theories (<a href="physicist#john-c-baez">John C. Baez</a>)</li><li id="_362"><a href="#quantum-field-theory-for-the-gifted-amateur-by-tom-lancaster-2015">quantum Field Theory for The Gifted Amateur by Tom Lancaster (2015)</a></li></ul></div></div><div class="h" id="quantum-field-theory-lecture-notes"><div class="notnav"><h3><a href="quantum-field-theory-lecture-notes">Quantum field theory lecture notes</a></h3><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-notes"></a><span class="metrics"><span class="wcntr"> Words: 318</span><span class="dcnt"> Articles: 3</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-bibliography" class="u"> Quantum field theory bibliography</a><a href="#_toc/quantum-field-theory-lecture-notes" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-notes"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_363">Lecture notes found by <a href="google">Googling</a> "quantum field theory pdf":<div class="list"><ul id="_364"><li id="_365"><a href="https://www.ppd.stfc.ac.uk/Pages/Dasgupta_08_Intro_to_QFT.pdf">www.ppd.stfc.ac.uk/Pages/Dasgupta_08_Intro_to_QFT.pdf</a> "An Introduction to Quantum Field Theory" by Mrinal Dasgupta from the University of Manchester (2008). 48 pages.</li><li id="_366"><a href="https://www.thphys.uni-heidelberg.de/~weigand/QFT2-14/SkriptQFT2.pdf">www.thphys.uni-heidelberg.de/~weigand/QFT2-14/SkriptQFT2.pdf</a> "Quantum Field Theory I + II" by Timo Weigand from the Heidelberg University. Unknown year, references up to 2008.</li><li id="_367"><a href="https://edu.itp.phys.ethz.ch/hs12/qft1/">edu.itp.phys.ethz.ch/hs12/qft1/</a> Quantum Field Theory 1 by Niklas Beisert</li></ul></div></div><div class="h" id="an-introduction-to-qed-and-qcd-by-jeff-forshaw-1997"><div class="notnav"><h4><a href="an-introduction-to-qed-and-qcd-by-jeff-forshaw-1997">An Introduction to QED and QCD by Jeff Forshaw (1997)</a></h4><span class="hover-meta"> <a class="split" href="an-introduction-to-qed-and-qcd-by-jeff-forshaw-1997"></a><span class="metrics"><span class="wcntr"> Words: 10</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-notes" class="u"> Quantum field theory lecture notes</a><a href="#_toc/an-introduction-to-qed-and-qcd-by-jeff-forshaw-1997" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/an-introduction-to-qed-and-qcd-by-jeff-forshaw-1997"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_368"><a href="http://www.hep.man.ac.uk/u/forshaw/NorthWest/QED.pdf">www.hep.man.ac.uk/u/forshaw/NorthWest/QED.pdf</a> <a href="https://web.archive.org/web/20200824083133/http://www.hep.man.ac.uk/u/forshaw/NorthWest/QED.pdf">web.archive.org/web/20200824083133/http://www.hep.man.ac.uk/u/forshaw/NorthWest/QED.pdf</a></div><div class="p" id="_369">These seem very direct and not ultra advanced, good read.</div><div class="h" id="quantum-field-theory-lecture-notes-by-david-tong-2007"><div class="notnav"><h4><a href="quantum-field-theory-lecture-notes-by-david-tong-2007">Quantum Field Theory lecture notes by David Tong (2007)</a></h4><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-notes-by-david-tong-2007"></a><span class="metrics"><span class="wcntr"> Words: 162</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-notes" class="u"> Quantum field theory lecture notes</a><a href="#_toc/quantum-field-theory-lecture-notes-by-david-tong-2007" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-notes-by-david-tong-2007"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="physicist#david-tong">David Tong</a></span></div></nav></div><div class="p" id="_371"><a href="https://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf">www.damtp.cam.ac.uk/user/tong/qft/qft.pdf</a></div><div class="p" id="_372">Author: <a href="physicist#david-tong">David Tong</a>.</div><div class="p" id="_373">Number of pages circa 2021: 155.</div><div class="p" id="_374">It should also be noted that those notes are still being updated circa 2020 much after original publication. But without <a href="software#git">Git</a> to track the <a href="computer#latex">LaTeX</a>, it is hard to be sure how much. <a href="ourbigbook-com">We'll get there one day, one day</a>.</div><div class="p" id="_375">Likely used at: <a href="#david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute">David Tong's 2009 Quantum Field Theory lectures at the Perimeter Institute</a>.</div><div class="p" id="_376">Some quotes self describing the work:<div class="list"><ul id="_377"><li id="_378"><div><blockquote id="_379"><div class="p" id="_380"><a href="#an-introduction-to-quantum-field-theory-by-peskin-and-schroeder-1995">an Introduction To Quantum Field Theory by Peskin and Schroeder (1995)</a></div><div class="p" id="_381">This is a very clear and comprehensive book, covering everything in this course at the right level. To a large extent, our course will follow the first section of this book.</div></blockquote></div>Perhaps for this reason <a href="ciro-santilli">Ciro Santilli</a> was not able to get as much as he'd out of those notes either. This is not to say that the notes are bad, just not what Ciro needed, much like P&S:<div class="list"><ul id="_382"><li id="_383"><a href="ciro-santilli#the-missing-link-between-basic-and-advanced">the missing link between basic and advanced</a></li><li id="_384"><a href="physics#doing-physics-means-calculating-a-number">doing physics means calculating a number</a></li></ul></div></li><li id="_385"><div><blockquote id="_386">In this course we will not discuss <a href="#path-integral-formulation">path integral methods</a>, and focus instead on <a href="#canonical-quantization">canonical quantization</a>.</blockquote></div></li></ul></div></div><div class="p" id="_387">A follow up course in the <a href="university#university-of-cambridge">University of Cambridge</a> seems to be the "Advanced QFT course" (AQFT, Quantum field theory II) by David Skinner: <a href="http://www.damtp.cam.ac.uk/user/dbs26/AQFT.html">www.damtp.cam.ac.uk/user/dbs26/AQFT.html</a></div><div class="h" id="quantum-field-theory-book-by-mark-srednicki-2006"><div class="notnav"><h4><a href="quantum-field-theory-book-by-mark-srednicki-2006">Quantum Field Theory book by Mark Srednicki (2006)</a></h4><span class="hover-meta"> <a class="split" href="quantum-field-theory-book-by-mark-srednicki-2006"></a><span class="metrics"><span class="wcntr"> Words: 94</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-notes" class="u"> Quantum field theory lecture notes</a><a href="#_toc/quantum-field-theory-book-by-mark-srednicki-2006" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-book-by-mark-srednicki-2006"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_388">Free to view draft: <a href="https://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf">web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf</a> Page presenting it: <a href="http://web.physics.ucsb.edu/~mark/qft.html">web.physics.ucsb.edu/~mark/qft.html</a></div><div class="p" id="_389">Author affiliation: University of California, Santa Barbara.</div><div class="p" id="_390">Number of pages: 616!</div><div class="p" id="_391">Don't redistribute clause, and final version by Cambridge University Press, alas, so corrections will never be merged back: <a href="http://web.physics.ucsb.edu/~mark/qft.html">web.physics.ucsb.edu/~mark/qft.html</a>. But at least he's collecing erratas for the published (and therefore draft) versions there.</div><div class="p" id="_392">The book is top-level organized in spin 0, spin half, and spin 1. Quite ominous, really.</div><div class="p" id="_393">The preface states that one of its pedagogical philosophies is to "Illustration of the basic concepts with the simplest examples.", so maybe there is hope after all.</div><div class="h" id="quantum-field-theory-lectures"><div class="notnav"><h3><a href="quantum-field-theory-lectures">Quantum field theory lectures</a></h3><span class="hover-meta"> <a class="split" href="quantum-field-theory-lectures"></a><span class="metrics"><span class="wcntr"> Words: 515</span><span class="dcnt"> Articles: 17</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-bibliography" class="u"> Quantum field theory bibliography</a><a href="#_toc/quantum-field-theory-lectures" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lectures"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="h" id="relativistic-quantum-mechanics-by-apoorva-d-patel-2014"><div class="notnav"><h4><a href="relativistic-quantum-mechanics-by-apoorva-d-patel-2014">Relativistic Quantum Mechanics by Apoorva D Patel (2014)</a></h4><span class="hover-meta"> <a class="split" href="relativistic-quantum-mechanics-by-apoorva-d-patel-2014"></a><span class="metrics"><span class="wcntr"> Words: 12</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lectures" class="u"> Quantum field theory lectures</a><a href="#_toc/relativistic-quantum-mechanics-by-apoorva-d-patel-2014" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/relativistic-quantum-mechanics-by-apoorva-d-patel-2014"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_394"><a href="https://www.youtube.com/playlist?list=PLbMVogVj5nJTDMhThY9xu2Tvg0u1RPuxO">www.youtube.com/playlist?list=PLbMVogVj5nJTDMhThY9xu2Tvg0u1RPuxO</a></div><div class="p" id="_395">45 1 hour lessons. The Indian traditional music opening is the best.</div><div class="h" id="new-revolutions-in-particle-physics-by-leonard-susskind-2009"><div class="notnav"><h4><a href="new-revolutions-in-particle-physics-by-leonard-susskind-2009">New Revolutions in Particle Physics by Leonard Susskind (2009)</a></h4><span class="hover-meta"> <a class="split" href="new-revolutions-in-particle-physics-by-leonard-susskind-2009"></a><span class="metrics"><span class="wcntr"> Words: 5</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lectures" class="u"> Quantum field theory lectures</a><a href="#_toc/new-revolutions-in-particle-physics-by-leonard-susskind-2009" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/new-revolutions-in-particle-physics-by-leonard-susskind-2009"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="physicist#lecture-by-leonard-susskind">Lecture by Leonard Susskind</a></span></div></nav></div><div class="p" id="_397"><a href="https://www.youtube.com/playlist?list=PL138995FAC49F5FB4">www.youtube.com/playlist?list=PL138995FAC49F5FB4</a></div><div class="p" id="_398">10 2-hour lessons.</div><div class="p" id="_399">Lecturer: <a href="physicist#leonard-susskind">Leonard Susskind</a>.</div><div class="h" id="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute"><div class="notnav"><h4><a href="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute">David Tong's 2009 Quantum Field Theory lectures at the Perimeter Institute</a></h4><span class="hover-meta"> <a class="split" href="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute"></a><span class="metrics"><span class="wcntr"> Words: 35</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lectures" class="u"> Quantum field theory lectures</a><a href="#_toc/david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="physicist#david-tong">David Tong</a></span></div></nav></div><div class="p" id="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/_401"><a href="https://www.youtube.com/playlist?list=PLaNkJORnlhZlVkrpQVvCTVvGAMIlXL88Y">www.youtube.com/playlist?list=PLaNkJORnlhZlVkrpQVvCTVvGAMIlXL88Y</a></div><div class="p" id="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/_402">Lecture notes: <a href="#quantum-field-theory-lecture-notes-by-david-tong-2007">Quantum Field Theory lecture notes by David Tong (2007)</a>.</div><div class="p" id="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/_403">By <a href="physicist#david-tong">David Tong</a>.</div><div class="p" id="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/_404">14 1 hours 20 minute lectures.</div><div class="p" id="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/_405">The video resolution is extremely low, with images glued as he moves away from what he wrote :-) The beauty of the early <a href="computer#internet">Internet</a>.</div><div class="h" id="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/lecture-1"><div class="notnav"><h5><a href="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/lecture-1">Lecture 1</a></h5><span class="hover-meta"> <a class="split" href="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/lecture-1"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute" class="u"> David Tong's 2009 Quantum Field Theory lectures at the Perimeter Institute</a><a href="#_toc/david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/lecture-1" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/lecture-1"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="david-tong-s-2009-quantum-field-theory-lectures-at-the-perimeter-institute/_406"><a href="https://www.youtube.com/watch?v=H3AFzbrqH68">www.youtube.com/watch?v=H3AFzbrqH68</a></div><div class="h" id="quantum-field-theory-courses-by-tobias-osborne"><div class="notnav"><h4><a href="quantum-field-theory-courses-by-tobias-osborne">Quantum field theory courses by Tobias Osborne</a></h4><span class="hover-meta"> <a class="split" href="quantum-field-theory-courses-by-tobias-osborne"></a><span class="metrics"><span class="wcntr"> Words: 463</span><span class="dcnt"> Articles: 12</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lectures" class="u"> Quantum field theory lectures</a><a href="#_toc/quantum-field-theory-courses-by-tobias-osborne" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-courses-by-tobias-osborne"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="physicist#tobias-j-osborne">Tobias J. Osborne</a></span></div></nav></div><div class="h" id="quantum-field-theory-lecture-by-tobias-osborne-2017"><div class="notnav"><h5><a href="quantum-field-theory-lecture-by-tobias-osborne-2017">Quantum field theory lecture by Tobias Osborne (2017)</a></h5><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017"></a><span class="metrics"><span class="wcntr"> Words: 439</span><span class="dcnt"> Articles: 9</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-courses-by-tobias-osborne" class="u"> Quantum field theory courses by Tobias Osborne</a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-by-tobias-osborne-2017"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_408"><a href="https://www.youtube.com/playlist?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS">www.youtube.com/playlist?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS</a></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_409">This is a bit "<a href="physics#how-to-teach-and-learn-physics">formal hocus pocus first, action later</a>". But withing that category, it is just barely basic enough that 2021 Ciro can understand something.</div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_410">By: <a href="physicist#tobias-j-osborne">Tobias J. Osborne</a>.</div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_411">Lecture notes transcribed by a student: <a href="https://github.com/avstjohn/qft">github.com/avstjohn/qft</a></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_412">18 1h30 lectures.</div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_413">Followup course: <a href="#advanced-quantum-field-theory-lecture-by-tobias-osborne-2017">Advanced quantum field theory lecture by Tobias Osborne (2017)</a>.</div><div class="h" id="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-1"><div class="notnav"><h6><a href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-1">Lecture 1</a></h6><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-1"></a><span class="metrics"><span class="wcntr"> Words: 146</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-1" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-1"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_414"><a href="https://www.youtube.com/watch?v=T58H6ofIOpE">www.youtube.com/watch?v=T58H6ofIOpE</a></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_415">Bibliography review:<div class="list"><ul id="quantum-field-theory-lecture-by-tobias-osborne-2017/_416"><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_417"><a href="#quantum-field-theory-lecture-notes-by-david-tong-2007">Quantum Field Theory lecture notes by David Tong (2007)</a> is the course basis</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_418"><a href="#quantum-field-theory-in-a-nutshell-by-anthony-zee-2010">quantum field theory in a nutshell by Anthony Zee (2010)</a> is a good quick and dirty book to start</li></ul></div></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_419">Course outline given:<div class="list"><ul id="quantum-field-theory-lecture-by-tobias-osborne-2017/_420"><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_421">classical field theory</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_422">quantum scalar field. Covers <a href="relativistic-quantum-mechanics#boson">bosons</a>, and is simpler to get intuition about.</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_423">quantum Dirac field. Covers <a href="relativistic-quantum-mechanics#fermion">fermions</a></li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_424">interacting fields</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_425"><a href="mathematics#perturbation-theory">perturbation theory</a></li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_426"><a href="#renormalization">renormalization</a></li></ul></div></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_427">Non-relativistic <a href="">QFT</a> is a limit of relativistic QFT, and can be used to describe for example <a href="condensed-matter-physics">condensed matter physics</a> systems at very low temperature. But it is still very hard to make accurate measurements even in those experiments.</div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_428">Defines "relativistic" as: "the <a href="mechanics#lagrangian">Lagrangian</a> is symmetric under the <a href="geometry#poincare-group">Poincaré group</a>".</div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_429">Mentions that "QFT is hard" because (a finite list follows???):<div><blockquote id="quantum-field-theory-lecture-by-tobias-osborne-2017/_430">There are no nontrivial finite-dimensional unitary <a href="geometry#representation-theory">representations</a> of the <a href="geometry#poincare-group">Poincaré group</a>.</blockquote></div>But I guess that if you fully understand what that means precisely, QTF won't be too hard for you!</div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_431">Notably, this is stark contrast with rotation symmetry groups (<a href="geometry#special-orthogonal-group">SO(3)</a>) which appears in space rotations present in <a href="quantum-mechanics#non-relativistic-quantum-mechanics">non-relativistic quantum mechanics</a>.</div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_432"><a href="https://www.youtube.com/watch?v=T58H6ofIOpE&t=5097">www.youtube.com/watch?v=T58H6ofIOpE&t=5097</a> describes the <a href="relativistic-quantum-mechanics#relativistic-particle-in-a-box-thought-experiment">relativistic particle in a box thought experiment</a> with shrinking walls</div><div class="h" id="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2"><div class="notnav"><h6><a href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2">Lecture 2</a></h6><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2"></a><span class="metrics"><span class="wcntr"> Words: 60</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_433"><a href="https://www.youtube.com/watch?v=bTcFOE5vpOA&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=2">www.youtube.com/watch?v=bTcFOE5vpOA&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=2</a></div><div class="list"><ul id="quantum-field-theory-lecture-by-tobias-osborne-2017/_434"><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_435">the advantage of using <a href="mechanics#lagrangian-mechanics">Lagrangian mechanics</a> instead of directly trying to work out the equations of motion is that it is easier to guess the Lagrangian correctly, while still imposing some fundamental constraints</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_436"><a href="https://youtu.be/bTcFOE5vpOA?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3375">youtu.be/bTcFOE5vpOA?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3375</a><div class="list"><ul id="quantum-field-theory-lecture-by-tobias-osborne-2017/_437"><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_438"><a href="mechanics#lagrangian-mechanics">Lagrangian mechanics</a> is better for <a href="#path-integral-formulation">path integral formulation</a>. But the <a href="mathematics">mathematics</a> of that is fuzzy, so not going in that path.</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_439"><a href="mechanics#hamiltonian-mechanics">Hamiltonian mechanics</a> is better for non-<a href="#path-integral-formulation">path integral formulation</a></li></ul></div></li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_440"><a href="https://youtu.be/bTcFOE5vpOA?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3449">youtu.be/bTcFOE5vpOA?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3449</a> Hamiltonian formalism requires finding conjugate pairs, and doing a </li></ul></div><div class="h" id="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-3"><div class="notnav"><h6><a href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-3">Lecture 3</a></h6><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-3"></a><span class="metrics"><span class="wcntr"> Words: 129</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-3" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-3"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_441"><a href="https://www.youtube.com/watch?v=cj-QpsZsDDY&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=3">www.youtube.com/watch?v=cj-QpsZsDDY&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=3</a></div><div class="list"><ul id="quantum-field-theory-lecture-by-tobias-osborne-2017/_442"><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_443">symmetry in classical field theory</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_444">from Lagrangian density we can algorithmically get equations of motion, but the Lagrangian density is a more compact way of representing the equations of motion</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_445">definition of symmetry in context: keeps Lagrangian unchanged up to a total derivative</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_446"><a href="mechanics#noether-s-theorem">Noether's theorem</a></li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_447"><a href="https://youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3062">youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3062</a> Lagrangian and conservation example under translations</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_448"><a href="https://youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3394">youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3394</a> same but for <a href="geometry#poincare-group">Poincaré transformations</a> But now things are harder, because it is harder to describe general infinitesimal Poincare transforms than it was to describe the translations. Using constraints/definition of Lorentz transforms, also constricts the allowed infinitesimal symmetries to 6 independent parameters</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_449"><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_450"><a href="https://youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=4525">youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=4525</a> brings out <a href="mechanics#poisson-bracket">Poisson brackets</a>, and concludes that each conserved current maps to a <a href="geometry#generator-of-a-lie-algebra">generator of the Lie algebra</a></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_451">This allows you to build the symmetry back from the conserved charges, just as you can determine conserved charges starting from the symmetry.</div></li></ul></div><div class="h" id="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-4"><div class="notnav"><h6><a href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-4">Lecture 4</a></h6><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-4"></a><span class="metrics"><span class="wcntr"> Words: 46</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-4" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-4"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_452"><a href="https://www.youtube.com/watch?v=fnMcaq6QqTY&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=4">www.youtube.com/watch?v=fnMcaq6QqTY&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=4</a></div><div class="list"><ul id="quantum-field-theory-lecture-by-tobias-osborne-2017/_453"><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_454">quantization. Uses a more or less standard way to guess the quantized system from the classical one using <a href="mechanics#hamiltonian-mechanics">Hamiltonian mechanics</a>.</li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_455"><a href="https://youtu.be/fnMcaq6QqTY?t=1179">youtu.be/fnMcaq6QqTY?t=1179</a> remembers how to solve the non-field <a href="quantum-mechanics#quantum-harmonic-oscillator">quantum harmonic oscillator</a></li><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_456"><a href="https://youtu.be/fnMcaq6QqTY?t=2008">youtu.be/fnMcaq6QqTY?t=2008</a> puts hats on everything to make the field version of things. With the <a href="relativistic-quantum-mechanics#klein-gordon-equation">Klein-Gordon equation</a> <a href="mechanics#hamiltonian-mechanics">Hamiltonian</a>, everything is analogous to the harmonic oscilator</li></ul></div><div class="h" id="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-5"><div class="notnav"><h6><a href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-5">Lecture 5</a></h6><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-5"></a><span class="metrics"><span class="wcntr"> Words: 10</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-5" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-5"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_457"><a href="https://www.youtube.com/watch?v=fnMcaq6QqTY&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=5">www.youtube.com/watch?v=fnMcaq6QqTY&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=5</a></div><div class="list"><ul id="quantum-field-theory-lecture-by-tobias-osborne-2017/_458"><li id="quantum-field-theory-lecture-by-tobias-osborne-2017/_459">something about finding a unitary representation of the poincare group</li></ul></div><div class="h" id="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-8"><div class="notnav"><h6><a href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-8">Lecture 8</a></h6><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-8"></a><span class="metrics"><span class="wcntr"> Words: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-8" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-8"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_460"><a href="https://www.youtube.com/watch?v=ARes2YJNFds&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=8">www.youtube.com/watch?v=ARes2YJNFds&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=8</a></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_461">Interactions.</div><div class="h" id="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-9"><div class="notnav"><h6><a href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-9">Lecture 9</a></h6><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-9"></a><span class="metrics"><span class="wcntr"> Words: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-9" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-9"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_462"><a href="https://www.youtube.com/watch?v=zSSjgG9AbgM&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=9">www.youtube.com/watch?v=zSSjgG9AbgM&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=9</a></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_463"><a href="#feynman-diagram">Feynman diagram</a>.</div><div class="h" id="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-14"><div class="notnav"><h6><a href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-14">Lecture 14</a></h6><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-14"></a><span class="metrics"><span class="wcntr"> Words: 2</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-14" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-14"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_464"><a href="https://www.youtube.com/watch?v=zSSjgG9AbgM&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=9">www.youtube.com/watch?v=zSSjgG9AbgM&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=9</a></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_465">Dirac field.</div><div class="h" id="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-15"><div class="notnav"><h6><a href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-15">Lecture 15</a></h6><span class="hover-meta"> <a class="split" href="quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-15"></a><span class="metrics"><span class="wcntr"> Words: 2</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Quantum field theory lecture by Tobias Osborne (2017)</a><a href="#_toc/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-15" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-15"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_466"><a href="https://www.youtube.com/watch?v=J2lV8uNx0LU&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=15">www.youtube.com/watch?v=J2lV8uNx0LU&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=15</a></div><div class="p" id="quantum-field-theory-lecture-by-tobias-osborne-2017/_467">Dirac equation.</div><div class="h" id="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017"><div class="notnav"><h5><a href="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017">Advanced quantum field theory lecture by Tobias Osborne (2017)</a></h5><span class="hover-meta"> <a class="split" href="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017"></a><span class="metrics"><span class="wcntr"> Words: 24</span><span class="dcnt"> Articles: 1</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-courses-by-tobias-osborne" class="u"> Quantum field theory courses by Tobias Osborne</a><a href="#_toc/advanced-quantum-field-theory-lecture-by-tobias-osborne-2017" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/advanced-quantum-field-theory-lecture-by-tobias-osborne-2017"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="physicist#tobias-j-osborne">Tobias J. Osborne</a></span></div></nav></div><div class="p" id="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/_469"><a href="https://www.youtube.com/playlist?list=PLDfPUNusx1ErSu1JDVV1KKGQkJQCkzL9u">www.youtube.com/playlist?list=PLDfPUNusx1ErSu1JDVV1KKGQkJQCkzL9u</a></div><div class="p" id="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/_470">Followup to <a href="#quantum-field-theory-lecture-by-tobias-osborne-2017">Quantum field theory lecture by Tobias Osborne (2017)</a>.</div><div class="p" id="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/_471">When the word "advanced" precedes QFT, you know that the brainrape is imminent!!!</div><div class="p" id="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/_472">Big goal: explain the <a href="standard-model">Standard Model</a>.</div><div class="h" id="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2"><div class="notnav"><h6><a href="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2">Lecture 2</a></h6><span class="hover-meta"> <a class="split" href="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2"></a><span class="metrics"><span class="wcntr"> Words: 3</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#advanced-quantum-field-theory-lecture-by-tobias-osborne-2017" class="u"> Advanced quantum field theory lecture by Tobias Osborne (2017)</a><a href="#_toc/advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-2"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/_473"><a href="https://www.youtube.com/watch?v=hapYr6rX4JM&list=PLDfPUNusx1ErSu1JDVV1KKGQkJQCkzL9u&index=2">www.youtube.com/watch?v=hapYr6rX4JM&list=PLDfPUNusx1ErSu1JDVV1KKGQkJQCkzL9u&index=2</a></div><div class="p" id="advanced-quantum-field-theory-lecture-by-tobias-osborne-2017/_474">Gaussian path integrals.</div><div class="h" id="quantum-field-theory-book"><div class="notnav"><h3><a href="quantum-field-theory-book">Quantum field theory book</a></h3><span class="hover-meta"> <a class="split" href="quantum-field-theory-book"></a><span class="metrics"><span class="wcntr"> Words: 232</span><span class="dcnt"> Articles: 7</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-bibliography" class="u"> Quantum field theory bibliography</a><a href="#_toc/quantum-field-theory-book" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-book"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="list"><ul id="_475"><li id="_476"><a href="https://web.archive.org/web/20150623011722/http://users.physik.fu-berlin.de/~kleinert/b6/psfiles/qft.pdf">web.archive.org/web/20150623011722/http://users.physik.fu-berlin.de/~kleinert/b6/psfiles/qft.pdf</a> by <a href="https://en.wikipedia.org/wiki/Hagen_Kleinert">Hagen Kleinert</a> (2015). 1500 pages!</li><li id="_477">The Quantum Theory of Fields by Steven Weinberg (2013) <a href="https://www.cambridge.org/core/books/quantum-theory-of-fields/22986119910BF6A2EFE42684801A3BDF">www.cambridge.org/core/books/quantum-theory-of-fields/22986119910BF6A2EFE42684801A3BDF</a> </li><li id="_478">Quantum Field Theory by Lewis H. Ryder 2nd edition (1996) <a href="https://www.amazon.co.uk/Quantum-Field-Theory-Lewis-Ryder/dp/0521478146">www.amazon.co.uk/Quantum-Field-Theory-Lewis-Ryder/dp/0521478146</a></li><li id="_479">Lectures of Quantum Field Theory by Ashok Das (2018) <a href="https://www.amazon.co.uk/Lectures-Quantum-Field-Theory-Ashok-ebook/dp/B07CL8Y3KY">www.amazon.co.uk/Lectures-Quantum-Field-Theory-Ashok-ebook/dp/B07CL8Y3KY</a></li><li id="_480">A Modern Introduction to Quantum Field Theory by Michele Maggiore (2005) <a href="https://www.amazon.co.uk/Modern-Introduction-Quantum-Theory-Physics/dp/0198520743">www.amazon.co.uk/Modern-Introduction-Quantum-Theory-Physics/dp/0198520743</a></li></ul></div><div class="h" id="no-nonsense-quantum-field-theory-by-jakob-schwichtenberg-2020"><div class="notnav"><h4><a href="no-nonsense-quantum-field-theory-by-jakob-schwichtenberg-2020">No-Nonsense Quantum Field Theory by Jakob Schwichtenberg (2020)</a></h4><span class="hover-meta"> <a class="split" href="no-nonsense-quantum-field-theory-by-jakob-schwichtenberg-2020"></a><span class="metrics"><span class="wcntr"> Words: 48</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-book" class="u"> Quantum field theory book</a><a href="#_toc/no-nonsense-quantum-field-theory-by-jakob-schwichtenberg-2020" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/no-nonsense-quantum-field-theory-by-jakob-schwichtenberg-2020"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a><span class="tags"> Tags: <a href="physicist#jakob-schwichtenberg">Jakob Schwichtenberg</a></span></div></nav></div><div class="p" id="_482"><a href="https://www.amazon.com/No-Nonsense-Quantum-Field-Theory-Student-Friendly/dp/3948763011">www.amazon.com/No-Nonsense-Quantum-Field-Theory-Student-Friendly/dp/3948763011</a></div><div class="p" id="_483">This book really tries to recall basic things to ensure that the reader will be able to understand the more advanced ones.</div><div class="p" id="_484">Sometimes it goes a little bit overboard, like defining what a <a href="formalization-of-mathematics#function-mathematics">function</a> does several times.</div><div class="p" id="_485">But <a href="ciro-santilli">Ciro Santilli</a> really prefers it when authors error on the side of obvious.</div><div class="h" id="quantum-field-theory-for-the-gifted-amateur-by-tom-lancaster-2015"><div class="notnav"><h4><a href="quantum-field-theory-for-the-gifted-amateur-by-tom-lancaster-2015">Quantum Field Theory for The Gifted Amateur by Tom Lancaster (2015)</a></h4><span class="hover-meta"> <a class="split" href="quantum-field-theory-for-the-gifted-amateur-by-tom-lancaster-2015"></a><span class="metrics"><span class="wcntr"> Words: 17</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-book" class="u"> Quantum field theory book</a><a href="#_toc/quantum-field-theory-for-the-gifted-amateur-by-tom-lancaster-2015" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-for-the-gifted-amateur-by-tom-lancaster-2015"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_486"><a href="https://www.amazon.co.uk/Quantum-Field-Theory-Gifted-Amateur/dp/019969933X">www.amazon.co.uk/Quantum-Field-Theory-Gifted-Amateur/dp/019969933X</a></div><div class="p" id="_487">People are mostly saying you have to be a more of a genius amateur to read it.</div><div class="h" id="student-friendly-quantum-field-theory-by-robert-d-klauber-2013"><div class="notnav"><h4><a href="student-friendly-quantum-field-theory-by-robert-d-klauber-2013">Student Friendly Quantum Field Theory by Robert D Klauber (2013)</a></h4><span class="hover-meta"> <a class="split" href="student-friendly-quantum-field-theory-by-robert-d-klauber-2013"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-book" class="u"> Quantum field theory book</a><a href="#_toc/student-friendly-quantum-field-theory-by-robert-d-klauber-2013" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/student-friendly-quantum-field-theory-by-robert-d-klauber-2013"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_488"><a href="http://www.quantumfieldtheory.info/">www.quantumfieldtheory.info/</a></div><div class="p" id="_489"><a href="https://www.quora.com/Whats-an-expert-opinion-on-Robert-Klaubers-Student-Friendly-Quantum-Field-Theory">www.quora.com/Whats-an-expert-opinion-on-Robert-Klaubers-Student-Friendly-Quantum-Field-Theory</a></div><div class="p" id="_490"><a href="https://www.amazon.co.uk/Student-Friendly-Quantum-Field-Theory/dp/0984513957">www.amazon.co.uk/Student-Friendly-Quantum-Field-Theory/dp/0984513957</a></div><div class="h" id="quantum-field-theory-in-a-nutshell-by-anthony-zee-2010"><div class="notnav"><h4><a href="quantum-field-theory-in-a-nutshell-by-anthony-zee-2010">Quantum field theory in a nutshell by Anthony Zee (2010)</a></h4><span class="hover-meta"> <a class="split" href="quantum-field-theory-in-a-nutshell-by-anthony-zee-2010"></a><span class="metrics"><span class="wcntr"> Words: 37</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-book" class="u"> Quantum field theory book</a><a href="#_toc/quantum-field-theory-in-a-nutshell-by-anthony-zee-2010" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-in-a-nutshell-by-anthony-zee-2010"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_491">Author: <a href="https://en.wikipedia.org/wiki/Anthony_Zee">en.wikipedia.org/wiki/Anthony_Zee</a> from <a href="university#university-of-california-santa-barbara">University of California, Santa Barbara</a>.</div><div class="p" id="_492">ISBN-13: 978-0691140346</div><div class="p" id="_493"><a href="amazon">Amazon</a>: <a href="https://www.amazon.com/dp/0691140340">www.amazon.com/dp/0691140340</a></div><div class="p" id="_494"><a href="#quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-1">lecture 1</a> mentions that this book is quick and dirty, as one might guess from the title. <a href="ciro-santilli">Ciro Santilli</a> thinks he's gonna like this one.</div><div class="p" id="_495">First edition: from 2003, <a href="https://www.amazon.com/dp/0691010196">www.amazon.com/dp/0691010196</a>, ISBN-13: 978-0691010199.</div><div class="p" id="_496">Summary:<div class="list"><ul id="_497"><li id="_498">page 8: <a href="#infinitely-many-slits-thought-experiment">infinitely many slits thought experiment</a></li></ul></div></div><div class="h" id="problem-book-in-quantum-field-theory-by-voja-radovanovic-2008"><div class="notnav"><h4><a href="problem-book-in-quantum-field-theory-by-voja-radovanovic-2008">Problem Book in Quantum Field Theory by Voja Radovanovic (2008)</a></h4><span class="hover-meta"> <a class="split" href="problem-book-in-quantum-field-theory-by-voja-radovanovic-2008"></a></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-book" class="u"> Quantum field theory book</a><a href="#_toc/problem-book-in-quantum-field-theory-by-voja-radovanovic-2008" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/problem-book-in-quantum-field-theory-by-voja-radovanovic-2008"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_499"><a href="https://www.springer.com/gp/book/9783540770138">www.springer.com/gp/book/9783540770138</a></div><div class="h" id="quantum-field-theory-demystified-by-david-mcmahon-2008"><div class="notnav"><h4><a href="quantum-field-theory-demystified-by-david-mcmahon-2008">Quantum Field Theory Demystified by David McMahon (2008)</a></h4><span class="hover-meta"> <a class="split" href="quantum-field-theory-demystified-by-david-mcmahon-2008"></a><span class="metrics"><span class="wcntr"> Words: 46</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-book" class="u"> Quantum field theory book</a><a href="#_toc/quantum-field-theory-demystified-by-david-mcmahon-2008" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/quantum-field-theory-demystified-by-david-mcmahon-2008"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_500">This didn't really deliver. It does start from the basics, but it is often hard to link those basics to more interesting or deeper points. Also like many other <a href="#quantum-field-theory-book">Quantum field theory book</a>, it does not seem to contain a single comparison between a theoretical result and an experiment.</div><div class="h" id="an-introduction-to-quantum-field-theory-by-peskin-and-schroeder-1995"><div class="notnav"><h4><a href="an-introduction-to-quantum-field-theory-by-peskin-and-schroeder-1995">An Introduction To Quantum Field Theory by Peskin and Schroeder (1995)</a></h4><span class="hover-meta"> <a class="split" href="an-introduction-to-quantum-field-theory-by-peskin-and-schroeder-1995"></a><span class="metrics"><span class="wcntr"> Words: 39</span></span></span></div><nav class="h-nav h-nav-toplevel"><div class="nav"><a href="#quantum-field-theory-book" class="u"> Quantum field theory book</a><a href="#_toc/an-introduction-to-quantum-field-theory-by-peskin-and-schroeder-1995" class="toc"></a><a href="https://ourbigbook.com/cirosantilli/an-introduction-to-quantum-field-theory-by-peskin-and-schroeder-1995"><img src="_obb/logo.svg" class="logo" /> OurBigBook.com</a></div></nav></div><div class="p" id="_501"><a href="https://www.amazon.co.uk/Introduction-Quantum-Theory-Frontiers-Physics/dp/0201503972">www.amazon.co.uk/Introduction-Quantum-Theory-Frontiers-Physics/dp/0201503972</a></div><div class="p" id="_502">This is very widely used in courses as of 2020, it became kind of the default book.</div><div class="p" id="_503">Unfortunately, this approach bores <a href="ciro-santilli">Ciro Santilli</a> to death. Or perhaps is too <a href="ciro-santilli#the-missing-link-between-basic-and-advanced">just advanced for him to appreciate</a>. Either of those.</div><div class="p" id="_504">800+ pages.</div><h2 id="_ancestors"><a href="#_ancestors"><span class="fa-solid-900 icon"></span> Ancestors <span class="meta">(7)</span></a></h2><div class="list"><ol><li><a href="relativistic-quantum-mechanics">Relativistic quantum mechanics</a></li><li><a href="quantum-mechanics">Quantum mechanics</a></li><li><a href="particle-physics">Particle physics</a></li><li><a href="physics">Physics</a></li><li><a href="science#natural-science">Natural science</a></li><li><a href="science">Science</a></li><li><a href="."><span title="Home" class="fa-solid-900 icon"></span> Home</a></li></ol></div><h2 id="_incoming-links"><a href="#_incoming-links"><span title="Incoming links" class="fa-solid-900 icon"></span> Incoming links <span class="meta">(21)</span></a></h2><div class="list"><ul><li><a href="website#coursera">Coursera</a></li><li><a href="physicist#david-tong">David Tong</a></li><li><a href="website#edx">EdX</a></li><li><a href="#effective-field-theory">Effective field theory</a></li><li><a href="mechanics#generalized-coordinate">Generalized coordinate</a></li><li><a href="#infinitely-many-slits-thought-experiment">Infinitely many slits thought experiment</a></li><li><a href="music#jazz-fusion">Jazz fusion</a></li><li><a href="mechanics#lagrangian-density">Lagrangian density</a></li><li><a href="mechanics#lagrangian-mechanics">Lagrangian mechanics</a></li><li><a href="art#luxury-goods">Luxury goods</a></li><li><a href="mathematics#millennium-prize-problems">Millennium Prize Problems</a></li><li><a href="mathematics#perturbation-theory">Perturbation theory</a></li><li><a href="physics#physics-education-needs-more-focus-on-understanding-experiments-and-their-history">Physics education needs more focus on understanding experiments and their history</a></li><li><a href="quantum-mechanics#quantization-of-a-real-scalar-field">Quantization of a real scalar field</a></li><li><a href="#quantum-chromodynamics">Quantum chromodynamics</a></li><li><a href="#quantum-electrodynamics">Quantum electrodynamics</a></li><li><a href="quantum-mechanics#quantum-mechanics-for-engineers-by-leon-van-dommelen-2011">Quantum Mechanics for Engineers by Leon van Dommelen (2011)</a></li><li><a href="#second-quantization">Second quantization</a></li><li><a href="quantum-mechanics#solutions-of-the-schrodinger-equation-for-two-electrons">Solutions of the Schrodinger equation for two electrons</a></li><li><a href="calculus#the-wave-equation-can-be-seen-as-infinitely-many-infinitesimal-coupled-oscillators">The wave equation can be seen as infinitely many infinitesimal coupled oscillators</a></li><li><a href="#what-does-it-mean-that-photons-are-force-carriers-for-electromagnetism">What does it mean that photons are force carriers for electromagnetism?</a></li></ul></div><h2 id="_synonyms"><a href="#_synonyms"><span title="Synonyms" class="fa-solid-900 icon"></span> Synonyms <span class="meta">(1)</span></a></h2><div class="list"><ul><li><a href="">QFT</a></li></ul></div> </main> <footer> <div>Powered by <a href="https://docs.ourbigbook.com">OurBigBook</a></div> <div>License: <a href="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA 4.0</a> unless noted</div> <div><a href="https://github.com/cirosantilli/cirosantilli.github.io/issues">Suggestions and corrections</a></div> <div><a href="contact">Contact Ciro Santilli</a></div> <div><a href="_dir">Website source code</a></div> <div><a href="https://github.com/cirosantilli/cirosantilli.github.io">Website source code on GitHub</a></div> <div><a href="_file/quantum-field-theory.bigb">Source code for this page: quantum-field-theory.bigb</a></div> <div><a href="https://github.com/cirosantilli/cirosantilli.github.io/blob/858d7eb936b541979660e3aecb7abf96541fc06c/quantum-field-theory.bigb">Source code for this page on GitHub</a></div> <div>Cite with: <a href="https://zenodo.org/badge/latestdoi/16453261">this DOI</a></div> <div><img src="https://raw.githubusercontent.com/cirosantilli/media/master/ID_photo_of_Ciro_Santilli_taken_in_2013_left_eye_200_100.jpg" loading="lazy" alt="ID photo of Ciro Santilli taken in 2013 right eye"></div> </footer> <script> window.ourbigbook_split_headers = true; 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