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xmlns:svg="http://www.w3.org/2000/svg" xml:lang="en" lang="en"> <head><meta http-equiv="Content-type" content="application/xhtml+xml;charset=utf-8" /><title>Contents</title></head> <body> <blockquote> under construction </blockquote> <div class="rightHandSide"> <div class="toc clickDown" tabindex="0"> <h3 id="context">Context</h3> <h4 id="physics">Physics</h4> <div class="hide"><div> <a class="existingWikiWord" href="/nlab/show/physics">physics</a>, <a class="existingWikiWord" href="/nlab/show/mathematical+physics">mathematical physics</a>, <a class="existingWikiWord" href="/nlab/show/philosophy+of+physics">philosophy of physics</a> <h2 id="surveys_textbooks_and_lecture_notes">Surveys, textbooks and lecture notes</h2> <ul> <li> <a class="existingWikiWord" href="/nlab/show/higher+category+theory+and+physics">(higher) category theory and physics</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/geometry+of+physics">geometry of physics</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/books+and+reviews+in+mathematical+physics">books and reviews</a>, <a class="existingWikiWord" href="/nlab/show/physics+resources">physics resources</a> </li> </ul> <hr /> <a class="existingWikiWord" href="/nlab/show/theory+%28physics%29">theory (physics)</a>, <a class="existingWikiWord" href="/nlab/show/model+%28physics%29">model (physics)</a> <a class="existingWikiWord" href="/nlab/show/experiment">experiment</a>, <a class="existingWikiWord" href="/nlab/show/measurement">measurement</a>, <a class="existingWikiWord" href="/nlab/show/computable+physics">computable physics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/mechanics">mechanics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/mass">mass</a>, <a class="existingWikiWord" href="/nlab/show/charge">charge</a>, <a class="existingWikiWord" href="/nlab/show/momentum">momentum</a>, <a class="existingWikiWord" href="/nlab/show/angular+momentum">angular momentum</a>, <a class="existingWikiWord" href="/nlab/show/moment+of+inertia">moment of inertia</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/dynamics+on+Lie+groups">dynamics on Lie groups</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/rigid+body+dynamics">rigid body dynamics</a></li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/field+%28physics%29">field (physics)</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Lagrangian+mechanics">Lagrangian mechanics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/configuration+space">configuration space</a>, <a class="existingWikiWord" href="/nlab/show/state">state</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/action+functional">action functional</a>, <a class="existingWikiWord" href="/nlab/show/Lagrangian">Lagrangian</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/covariant+phase+space">covariant phase space</a>, <a class="existingWikiWord" href="/nlab/show/Euler-Lagrange+equations">Euler-Lagrange equations</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/Hamiltonian+mechanics">Hamiltonian mechanics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/phase+space">phase space</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/symplectic+geometry">symplectic geometry</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Poisson+manifold">Poisson manifold</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/symplectic+manifold">symplectic manifold</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/symplectic+groupoid">symplectic groupoid</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/multisymplectic+geometry">multisymplectic geometry</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/n-symplectic+manifold">n-symplectic manifold</a></li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/spacetime">spacetime</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/smooth+Lorentzian+manifold">smooth Lorentzian manifold</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/special+relativity">special relativity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/general+relativity">general relativity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/gravity">gravity</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>, <a class="existingWikiWord" href="/nlab/show/dilaton+gravity">dilaton gravity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/black+hole">black hole</a> </li> </ul> </li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/classical+field+theory">Classical field theory</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/classical+physics">classical physics</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/classical+mechanics">classical mechanics</a></li> <li><a class="existingWikiWord" href="/nlab/show/waves">waves</a> and <a class="existingWikiWord" href="/nlab/show/optics">optics</a></li> <li><a class="existingWikiWord" href="/nlab/show/thermodynamics">thermodynamics</a></li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+mechanics">Quantum Mechanics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/quantum+mechanics+in+terms+of+dagger-compact+categories">in terms of ∞-compact categories</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+information">quantum information</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Hamiltonian+operator">Hamiltonian operator</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/density+matrix">density matrix</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Kochen-Specker+theorem">Kochen-Specker theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Bell%27s+theorem">Bell's theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Gleason%27s+theorem">Gleason's theorem</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantization">Quantization</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/geometric+quantization">geometric quantization</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/deformation+quantization">deformation quantization</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/path+integral">path integral quantization</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/semiclassical+approximation">semiclassical approximation</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">Quantum Field Theory</a> <ul> <li> Axiomatizations <ul> <li> <a class="existingWikiWord" href="/nlab/show/AQFT">algebraic QFT</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Wightman+axioms">Wightman axioms</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Haag-Kastler+axioms">Haag-Kastler axioms</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/operator+algebra">operator algebra</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/local+net">local net</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/conformal+net">conformal net</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Reeh-Schlieder+theorem">Reeh-Schlieder theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Osterwalder-Schrader+theorem">Osterwalder-Schrader theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/PCT+theorem">PCT theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Bisognano-Wichmann+theorem">Bisognano-Wichmann theorem</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/modular+theory">modular theory</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/spin-statistics+theorem">spin-statistics theorem</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/boson">boson</a>, <a class="existingWikiWord" href="/nlab/show/fermion">fermion</a></li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/FQFT">functorial QFT</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/cobordism">cobordism</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/%28%E2%88%9E%2Cn%29-category+of+cobordisms">(∞,n)-category of cobordisms</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/cobordism+hypothesis">cobordism hypothesis</a>-theorem </li> <li> <a class="existingWikiWord" href="/nlab/show/extended+topological+quantum+field+theory">extended topological quantum field theory</a> </li> </ul> </li> </ul> </li> <li> Tools <ul> <li> <a class="existingWikiWord" href="/nlab/show/perturbative+quantum+field+theory">perturbative quantum field theory</a>, <a class="existingWikiWord" href="/nlab/show/vacuum">vacuum</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/effective+quantum+field+theory">effective quantum field theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/renormalization">renormalization</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/BV-BRST+formalism">BV-BRST formalism</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/geometric+%E2%88%9E-function+theory">geometric ∞-function theory</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/particle+physics">particle physics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/phenomenology">phenomenology</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/model+%28in+particle+phyiscs%29">models</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/standard+model+of+particle+physics">standard model of particle physics</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/fields+and+quanta+-+table">fields and quanta</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/GUT">Grand Unified Theories</a>, <a class="existingWikiWord" href="/nlab/show/MSSM">MSSM</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/scattering+amplitude">scattering amplitude</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/on-shell+recursion">on-shell recursion</a>, <a class="existingWikiWord" href="/nlab/show/KLT+relations">KLT relations</a></li> </ul> </li> </ul> </li> <li> Structural phenomena <ul> <li> <a class="existingWikiWord" href="/nlab/show/universality+class">universality class</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+anomaly">quantum anomaly</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/Green-Schwarz+mechanism">Green-Schwarz mechanism</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/instanton">instanton</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/spontaneously+broken+symmetry">spontaneously broken symmetry</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Kaluza-Klein+mechanism">Kaluza-Klein mechanism</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/integrable+systems">integrable systems</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/holonomic+quantum+fields">holonomic quantum fields</a> </li> </ul> </li> <li> Types of quantum field thories <ul> <li> <a class="existingWikiWord" href="/nlab/show/TQFT">TQFT</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/2d+TQFT">2d TQFT</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Dijkgraaf-Witten+theory">Dijkgraaf-Witten theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Chern-Simons+theory">Chern-Simons theory</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/TCFT">TCFT</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/A-model">A-model</a>, <a class="existingWikiWord" href="/nlab/show/B-model">B-model</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/homological+mirror+symmetry">homological mirror symmetry</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/QFT+with+defects">QFT with defects</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/conformal+field+theory">conformal field theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/%281%2C1%29-dimensional+Euclidean+field+theories+and+K-theory">(1,1)-dimensional Euclidean field theories and K-theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/%282%2C1%29-dimensional+Euclidean+field+theory">(2,1)-dimensional Euclidean field theory and elliptic cohomology</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/CFT">CFT</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/WZW+model">WZW model</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/6d+%282%2C0%29-supersymmetric+QFT">6d (2,0)-supersymmetric QFT</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/gauge+theory">gauge theory</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/field+strength">field strength</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/gauge+group">gauge group</a>, <a class="existingWikiWord" href="/nlab/show/gauge+transformation">gauge transformation</a>, <a class="existingWikiWord" href="/nlab/show/gauge+fixing">gauge fixing</a> </li> <li> examples <ul> <li><a class="existingWikiWord" href="/nlab/show/electromagnetic+field">electromagnetic field</a>, <a class="existingWikiWord" href="/nlab/show/QED">QED</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/electric+charge">electric charge</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/magnetic+charge">magnetic charge</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yang-Mills+field">Yang-Mills field</a>, <a class="existingWikiWord" href="/nlab/show/QCD">QCD</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/Yang-Mills+theory">Yang-Mills theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/spinors+in+Yang-Mills+theory">spinors in Yang-Mills theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/topological+Yang-Mills+theory">topological Yang-Mills theory</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/Kalb-Ramond+field">Kalb-Ramond field</a></li> <li><a class="existingWikiWord" href="/nlab/show/supergravity+C-field">supergravity C-field</a></li> <li><a class="existingWikiWord" href="/nlab/show/RR+field">RR field</a></li> <li><a class="existingWikiWord" href="/nlab/show/first-order+formulation+of+gravity">first-order formulation of gravity</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/general+covariance">general covariance</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/D%27Auria-Fre+formulation+of+supergravity">D'Auria-Fre formulation of supergravity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/gravity+as+a+BF-theory">gravity as a BF-theory</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/sigma-model">sigma-model</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/particle">particle</a>, <a class="existingWikiWord" href="/nlab/show/relativistic+particle">relativistic particle</a>, <a class="existingWikiWord" href="/nlab/show/fundamental+particle">fundamental particle</a>, <a class="existingWikiWord" href="/nlab/show/spinning+particle">spinning particle</a>, <a class="existingWikiWord" href="/nlab/show/superparticle">superparticle</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/string">string</a>, <a class="existingWikiWord" href="/nlab/show/spinning+string">spinning string</a>, <a class="existingWikiWord" href="/nlab/show/superstring">superstring</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/membrane">membrane</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/AKSZ+theory">AKSZ theory</a> </li> </ul> </li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/string+theory">String Theory</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/string+theory+results+applied+elsewhere">string theory results applied elsewhere</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/number+theory+and+physics">number theory and physics</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/Riemann+hypothesis+and+physics">Riemann hypothesis and physics</a></li> </ul> </li> </ul> <div> <a href="/nlab/edit/physicscontents">Edit this sidebar</a> </div></div></div> <h4 id="quantum_field_theory">Quantum Field Theory</h4> <div class="hide"><div> <a class="existingWikiWord" href="/nlab/show/algebraic+quantum+field+theory">algebraic quantum field theory</a> (<a class="existingWikiWord" href="/nlab/show/perturbative+AQFT">perturbative</a>, <a class="existingWikiWord" href="/nlab/show/AQFT+on+curved+spacetime">on curved spacetimes</a>, <a class="existingWikiWord" href="/nlab/show/homotopical+algebraic+quantum+field+theory">homotopical</a>) <a class="existingWikiWord" href="/nlab/show/A+first+idea+of+quantum+field+theory">Introduction</a> <h2 id="concepts">Concepts</h2> <a class="existingWikiWord" href="/nlab/show/field+theory">field theory</a>: <ul> <li> <a class="existingWikiWord" href="/nlab/show/classical+field+theory">classical</a>, <a class="existingWikiWord" href="/nlab/show/prequantum+field+theory">pre-quantum</a>, <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">quantum</a>, <a class="existingWikiWord" href="/nlab/show/perturbative+quantum+field+theory">perturbative quantum</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/relativistic+field+theory">relativistic</a>, <a class="existingWikiWord" href="/nlab/show/Euclidean+field+theory">Euclidean</a>, <a class="existingWikiWord" href="/nlab/show/thermal+quantum+field+theory">thermal</a> </li> </ul> <a class="existingWikiWord" href="/nlab/show/Lagrangian+field+theory">Lagrangian field theory</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/field+%28physics%29">field (physics)</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/field+bundle">field bundle</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/field+history">field history</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/space+of+field+histories">space of field histories</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/Lagrangian+density">Lagrangian density</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Euler-Lagrange+form">Euler-Lagrange form</a>, <a class="existingWikiWord" href="/nlab/show/presymplectic+current">presymplectic current</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Euler-Lagrange+equations">Euler-Lagrange</a><a class="existingWikiWord" href="/nlab/show/equations+of+motion">equations of motion</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/locally+variational+field+theory">locally variational field theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/covariant+phase+space">covariant phase space</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Peierls-Poisson+bracket">Peierls-Poisson bracket</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/advanced+and+retarded+propagator">advanced and retarded propagator</a>, </li> <li> <a class="existingWikiWord" href="/nlab/show/causal+propagator">causal propagator</a> </li> </ul> </li> </ul> </li> </ul> <a class="existingWikiWord" href="/nlab/show/quantization">quantization</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/geometric+quantization">geometric quantization</a><a class="existingWikiWord" href="/nlab/show/geometric+quantization+of+symplectic+groupoids">of symplectic groupoids</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/algebraic+deformation+quantization">algebraic deformation quantization</a>, <a class="existingWikiWord" href="/nlab/show/star+algebra">star algebra</a> </li> </ul> <a class="existingWikiWord" href="/nlab/show/quantum+mechanical+system">quantum mechanical system</a>, <a class="existingWikiWord" href="/nlab/show/quantum+probability">quantum probability</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/subsystem">subsystem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/observables">observables</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/field+observables">field observables</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/local+observables">local observables</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/polynomial+observables">polynomial observables</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/microcausal+observables">microcausal observables</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/operator+algebra">operator algebra</a>, <a class="existingWikiWord" href="/nlab/show/C%2A-algebra">C*-algebra</a>, <a class="existingWikiWord" href="/nlab/show/von+Neumann+algebra">von Neumann algebra</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/local+net+of+observables">local net of observables</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/causal+locality">causal locality</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Haag-Kastler+axioms">Haag-Kastler axioms</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Wightman+axioms">Wightman axioms</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/field+net">field net</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/conformal+net">conformal net</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/state+on+a+star-algebra">state on a star-algebra</a>, <a class="existingWikiWord" href="/nlab/show/expectation+value">expectation value</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/pure+state">pure state</a> <a class="existingWikiWord" href="/nlab/show/wave+function">wave function</a> <a class="existingWikiWord" href="/nlab/show/collapse+of+the+wave+function">collapse of the wave function</a>/<a class="existingWikiWord" href="/nlab/show/conditional+expectation+value">conditional expectation value</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/mixed+state">mixed state</a>, <a class="existingWikiWord" href="/nlab/show/density+matrix">density matrix</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/space+of+quantum+states">space of quantum states</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/vacuum+state">vacuum state</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/quasi-free+state">quasi-free state</a>, </li> <li> <a class="existingWikiWord" href="/nlab/show/Hadamard+state">Hadamard state</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Wightman+propagator">Wightman propagator</a> </li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/picture+of+quantum+mechanics">picture of quantum mechanics</a> </li> </ul> <a class="existingWikiWord" href="/nlab/show/free+field">free field</a> <a class="existingWikiWord" href="/nlab/show/quantization">quantization</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/star+algebra">star algebra</a>, <a class="existingWikiWord" href="/nlab/show/Moyal+deformation+quantization">Moyal deformation quantization</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Wick+algebra">Wick algebra</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/canonical+commutation+relations">canonical commutation relations</a>, <a class="existingWikiWord" href="/nlab/show/Weyl+relations">Weyl relations</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/normal+ordered+product">normal ordered product</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/Fock+space">Fock space</a> </li> </ul> <a class="existingWikiWord" href="/nlab/show/gauge+theories">gauge theories</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/gauge+symmetry">gauge symmetry</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/BRST+complex">BRST complex</a>, <a class="existingWikiWord" href="/nlab/show/BV-BRST+formalism">BV-BRST formalism</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/local+BV-BRST+complex">local BV-BRST complex</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/BV-operator">BV-operator</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+master+equation">quantum master equation</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/master+Ward+identity">master Ward identity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/gauge+anomaly">gauge anomaly</a> </li> </ul> <a class="existingWikiWord" href="/nlab/show/interacting+field+theory">interacting field</a> <a class="existingWikiWord" href="/nlab/show/quantization">quantization</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/causal+perturbation+theory">causal perturbation theory</a>, <a class="existingWikiWord" href="/nlab/show/perturbative+AQFT">perturbative AQFT</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/interaction">interaction</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/S-matrix">S-matrix</a>, <a class="existingWikiWord" href="/nlab/show/scattering+amplitude">scattering amplitude</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/causal+additivity">causal additivity</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/time-ordered+product">time-ordered product</a>, <a class="existingWikiWord" href="/nlab/show/Feynman+propagator">Feynman propagator</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Feynman+diagram">Feynman diagram</a>, <a class="existingWikiWord" href="/nlab/show/Feynman+perturbation+series">Feynman perturbation series</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/effective+action">effective action</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/vacuum+stability">vacuum stability</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/interacting+field+algebra">interacting field algebra</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Bogoliubov%27s+formula">Bogoliubov's formula</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+M%C3%B8ller+operator">quantum Møller operator</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/adiabatic+limit">adiabatic limit</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/infrared+divergence">infrared divergence</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/interacting+vacuum">interacting vacuum</a> </li> </ul> </li> </ul> <a class="existingWikiWord" href="/nlab/show/renormalization">renormalization</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/renormalization+scheme">("re-")normalization scheme</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/extension+of+distributions">extension of distributions</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/renormalization+condition">("re"-)normalization condition</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+anomaly">quantum anomaly</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/renormalization+group">renormalization group</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/interaction+vertex+redefinition">interaction vertex redefinition</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/St%C3%BCckelberg-Petermann+renormalization+group">Stückelberg-Petermann renormalization group</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/renormalization+group+flow">renormalization group flow</a>/<a class="existingWikiWord" href="/nlab/show/running+coupling+constants">running coupling constants</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/effective+quantum+field+theory">effective quantum field theory</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/UV+cutoff">UV cutoff</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/counterterms">counterterms</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/relative+effective+action">relative effective action</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Wilsonian+RG">Wilsonian RG</a>, <a class="existingWikiWord" href="/nlab/show/Polchinski+flow+equation">Polchinski flow equation</a> </li> </ul> </li> </ul> <h2 id="Theorems">Theorems</h2> <h3 id="states_and_observables">States and observables</h3> <ul> <li> <a class="existingWikiWord" href="/nlab/show/order-theoretic+structure+in+quantum+mechanics">order-theoretic structure in quantum mechanics</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Alfsen-Shultz+theorem">Alfsen-Shultz theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Harding-D%C3%B6ring-Hamhalter+theorem">Harding-Döring-Hamhalter theorem</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/Kochen-Specker+theorem">Kochen-Specker theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Bell%27s+theorem">Bell's theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Fell%27s+theorem">Fell's theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Gleason%27s+theorem">Gleason's theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Wigner+theorem">Wigner theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Bub-Clifton+theorem">Bub-Clifton theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Kadison-Singer+problem">Kadison-Singer problem</a> </li> </ul> <h3 id="operator_algebra">Operator algebra</h3> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Wick%27s+theorem">Wick's theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/GNS+construction">GNS construction</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/cyclic+vector">cyclic vector</a>, <a class="existingWikiWord" href="/nlab/show/separating+vector">separating vector</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/modular+theory">modular theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Fell%27s+theorem">Fell's theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Stone-von+Neumann+theorem">Stone-von Neumann theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Haag%27s+theorem">Haag's theorem</a> </li> </ul> <h3 id="local_qft">Local QFT</h3> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Reeh-Schlieder+theorem">Reeh-Schlieder theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Bisognano-Wichmann+theorem">Bisognano-Wichmann theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/PCT+theorem">PCT theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/spin-statistics+theorem">spin-statistics theorem</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/DHR+superselection+theory">DHR superselection theory</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Osterwalder-Schrader+theorem">Osterwalder-Schrader theorem</a> (<a class="existingWikiWord" href="/nlab/show/Wick+rotation">Wick rotation</a>) </li> </ul> <h3 id="perturbative_qft">Perturbative QFT</h3> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Schwinger-Dyson+equation">Schwinger-Dyson equation</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/main+theorem+of+perturbative+renormalization">main theorem of perturbative renormalization</a> </li> </ul> </div></div> </div> </div> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#idea'>Idea</a></li> <li><a href='#properties'>Properties</a></li> <ul> <li><a href='#confinements'>Confinements</a></li> <li><a href='#asymptotic_freedom'>Asymptotic freedom</a></li> <li><a href='#trace_anomaly'>Trace anomaly</a></li> <li><a href='#PhaseDiagram'>Phase diagram</a></li> </ul> <li><a href='#related_concepts'>Related concepts</a></li> <li><a href='#references'>References</a></li> <ul> <li><a href='#general'>General</a></li> <li><a href='#Phases'>Phase diagram</a></li> <li><a href='#history'>History</a></li> <li><a href='#lattice_qcd'>Lattice QCD</a></li> <li><a href='#lightcone_quantization'>Light-cone quantization</a></li> </ul> </ul> </div> <h2 id="idea">Idea</h2> Quantum chromodynamics (“QCD”) is the <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">quantum field theory</a> of <a class="existingWikiWord" href="/nlab/show/Yang-Mills+theory">Yang-Mills theory</a>: it describes the <a class="existingWikiWord" href="/nlab/show/quantum+theory">quantum theory</a> of <a class="existingWikiWord" href="/nlab/show/gluons">gluons</a> and <a class="existingWikiWord" href="/nlab/show/quarks">quarks</a>. The corresponding <a class="existingWikiWord" href="/nlab/show/effective+field+theory">effective field theory</a> that describes <a class="existingWikiWord" href="/nlab/show/confinement">confined</a> <a class="existingWikiWord" href="/nlab/show/bound+states">bound states</a> such as <a class="existingWikiWord" href="/nlab/show/protons">protons</a> is <a class="existingWikiWord" href="/nlab/show/quantum+hadrodynamics">quantum hadrodynamics</a>. <h2 id="properties">Properties</h2> <h3 id="confinements">Confinements</h3> See at <a class="existingWikiWord" href="/nlab/show/confinement">confinement</a>. <h3 id="asymptotic_freedom">Asymptotic freedom</h3> See at <a class="existingWikiWord" href="/nlab/show/asymptotic+freedom">asymptotic freedom</a>. <h3 id="trace_anomaly">Trace anomaly</h3> See at <a class="existingWikiWord" href="/nlab/show/QCD+trace+anomaly">QCD trace anomaly</a>. <h3 id="PhaseDiagram">Phase diagram</h3> <a class="existingWikiWord" href="/nlab/show/QCD">QCD</a> has an intricate <a class="existingWikiWord" href="/nlab/show/phase+diagram">phase diagram</a> (e.g. <a href="#Shuryak96">Shuryak 96</a> <a href="#Hands01">Hands 01</a>, <a href="#Schaefer05">Schaefer 05</a>), phases including <ul> <li> <a class="existingWikiWord" href="/nlab/show/quark-gluon+plasma">quark-gluon plasma</a>, </li> <li> <a class="existingWikiWord" href="/nlab/show/colour+superconductivity">colour superconductivity</a>, </li> <li> … </li> </ul> <h2 id="related_concepts">Related concepts</h2> <ul> <li> <a class="existingWikiWord" href="/nlab/show/D%3D2+QCD">D=2 QCD</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/lattice+QCD">lattice QCD</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/super+QCD">super QCD</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/confinement">confinement</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/chiral+perturbation+theory">chiral perturbation theory</a>, <a class="existingWikiWord" href="/nlab/show/quantum+hadrodynamics">quantum hadrodynamics</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/quark+bag+model">quark bag model</a>, <a class="existingWikiWord" href="/nlab/show/Cheshire+cat+principle">Cheshire cat principle</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/AdS%2FQCD+correspondence">AdS/QCD correspondence</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/Gross-Neveu+model">Gross-Neveu model</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/QCD+cosmology">QCD cosmology</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">quantum field theory</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/gauge+theory">gauge theory</a> <ul> <li> <a class="existingWikiWord" href="/nlab/show/Yang-Mills+theory">Yang-Mills theory</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/quantization+of+Yang-Mills+theory">quantization of Yang-Mills theory</a></li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/QED">QED</a> </li> <li> QCD <ul> <li> <a class="existingWikiWord" href="/nlab/show/quark">quark</a>, <a class="existingWikiWord" href="/nlab/show/gluon">gluon</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/bound+states">bound states</a>: <a class="existingWikiWord" href="/nlab/show/glueballs">glueballs</a>, <a class="existingWikiWord" href="/nlab/show/hadrons">hadrons</a> (<a class="existingWikiWord" href="/nlab/show/mesons">mesons</a>, <a class="existingWikiWord" href="/nlab/show/baryons">baryons</a>) </li> <li> <a class="existingWikiWord" href="/nlab/show/colour+charge">colour charge</a>, <a class="existingWikiWord" href="/nlab/show/flavour+%28particle+physics%29">flavour (particle physics)</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/instanton+in+QCD">instanton in QCD</a>, <a class="existingWikiWord" href="/nlab/show/caloron">caloron</a>, <a class="existingWikiWord" href="/nlab/show/skyrmion">skyrmion</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/confinement">confinement</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/mass+gap">mass gap</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/quark-gluon+plasma">quark-gluon plasma</a> </li> <li> <a class="existingWikiWord" href="/nlab/show/colour+superconductivity">colour superconductivity</a> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/electroweak+field">electroweak field</a> </li> </ul> </li> </ul> </li> <li> <a class="existingWikiWord" href="/nlab/show/string+theory+results+applied+elsewhere">string theory results applied elsewhere</a> </li> </ul> <h2 id="references">References</h2> <h3 id="general">General</h3> Introduction and review: <ul> <li> <a class="existingWikiWord" href="/nlab/show/Jiri+Chyla">Jiri Chyla</a>, Quarks, partons and Quantum Chromodynamics, (<a href="http://inspirehep.net/record/674163/">spire:674163/)</a>, <a class="existingWikiWord" href="/nlab/files/ChylaQuarksQCD.pdf" title="pdf">pdf</a>) </li> <li> Peter Skands, Introduction to QCD (<a href="https://arxiv.org/abs/1207.2389">arXiv:1207.2389</a>, <a href="https://doi.org/10.1142/9789814525220_0008">doi:10.1142/9789814525220_0008</a>) </li> <li> Y. Kurihara, QCD at LHC for beginners Lesson 1 (<a href="http://www.iop.vast.ac.vn/theor/conferences/vsop/18/files/QCD_Kurihara_1.pdf">pdf</a>), Lesson 2 (<a href="http://www.iop.vast.ac.vn/theor/conferences/vsop/18/files/QCD_Kurihara_2.pdf">pdf</a>) Lesson 3 (<a href="http://www.iop.vast.ac.vn/theor/conferences/vsop/18/files/QCD_Kurihara_3.pdf">pdf</a>) </li> <li> <a class="existingWikiWord" href="/nlab/show/Particle+Data+Group">Particle Data Group</a>, Quantum Chromodynamics (<a href="http://pdg.lbl.gov/2015/reviews/rpp2015-rev-qcd.pdf">pdf</a>) </li> <li> <a class="existingWikiWord" href="/nlab/show/Franz+Gross">Franz Gross</a>, <a class="existingWikiWord" href="/nlab/show/Eberhard+Klempt">Eberhard Klempt</a> et al., 50 Years of Quantum Chromodynamics, EJPC [<a href="https://arxiv.org/abs/2212.11107">arXiv:2212.11107</a>] </li> </ul> Textbooks: <ul> <li> <a class="existingWikiWord" href="/nlab/show/Robert+E.+Marshak">Robert E. Marshak</a>, Chapter 5 of: Conceptual Foundations of Modern Particle Physics, World Scientific 1993 (<a href="https://doi.org/10.1142/1767">doi:10.1142/1767</a>) </li> <li> B. L. Ioffe , V. S. Fadin, L. N. Lipatov, Quantum Chromodynamics – Perturbative and Nonperturbative Aspects, Cambridge University Press (2010) (<a href="https://doi.org/10.1017/CBO9780511711817">doi:10.1017/CBO9780511711817</a>) </li> </ul> with emphasis on <a class="existingWikiWord" href="/nlab/show/phenomenology">phenomenology</a>: <ul> <li id="HalzenMartin84"><a class="existingWikiWord" href="/nlab/show/Francis+Halzen">Francis Halzen</a>, <a class="existingWikiWord" href="/nlab/show/Alan+Martin">Alan Martin</a>, Quarks and Leptons: An Introductory Course in Modern Particle Physics, Wiley 1984 (<a href="http://ajbell.web.cern.ch/ajbell/Documents/eBooks/Quarks%20&%20Leptons.pdf">pdf</a>)</li> </ul> On QCD’s <a class="existingWikiWord" href="/nlab/show/running+coupling+constant">running coupling constant</a>: <ul> <li><a class="existingWikiWord" href="/nlab/show/Alexandre+Deur">Alexandre Deur</a>, <a class="existingWikiWord" href="/nlab/show/Stanley+Brodsky">Stanley Brodsky</a>, <a class="existingWikiWord" href="/nlab/show/Guy+de+Teramond">Guy de Teramond</a>, The QCD Running Coupling, Prog. Part. Nuc. Phys. 90 1 (2016) (<a href="https://arxiv.org/abs/1604.08082">arXiv:1604.08082</a>, <a href="https://doi.org/10.1016/j.ppnp.2016.04.003">doi:10.1016/j.ppnp.2016.04.003</a>)</li> </ul> Rigorous construction as a <a class="existingWikiWord" href="/nlab/show/perturbative+quantum+field+theory">perturbative quantum field theory</a> via <a class="existingWikiWord" href="/nlab/show/causal+perturbation+theory">causal perturbation theory</a> is discussed in <ul> <li id="Scharf01"><a class="existingWikiWord" href="/nlab/show/G%C3%BCnter+Scharf">Günter Scharf</a>, chapter 3 of <a class="existingWikiWord" href="/nlab/show/Quantum+Gauge+Theories+--+A+True+Ghost+Story">Quantum Gauge Theories – A True Ghost Story</a>, Wiley 2001</li> </ul> Survey with emphasis on <a class="existingWikiWord" href="/nlab/show/non-perturbative+effects">non-perturbative effects</a>: <ul> <li id="Brambilla14"> Brambilla et al., <a class="existingWikiWord" href="/nlab/show/QCD+and+strongly+coupled+gauge+theories+-+challenges+and+perspectives">QCD and strongly coupled gauge theories - challenges and perspectives</a>, Eur Phys J C Part Fields. 2014; 74(10): 2981 (<a href="https://link.springer.com/article/10.1140%2Fepjc%2Fs10052-014-2981-5">doi:10.1140/epjc/s10052-014-2981-5</a>) </li> <li> Giorgio Comitini, Perturbative methods in non-perturbative Quantum Chromodynamics [<a href="https://arxiv.org/abs/2306.13624">arXiv:2306.13624</a>] </li> </ul> Discussion of on-shell methods in QCD <a class="existingWikiWord" href="/nlab/show/perturbation+theory">perturbation theory</a> includes <ul> <li><a class="existingWikiWord" href="/nlab/show/Zvi+Bern">Zvi Bern</a>, <a class="existingWikiWord" href="/nlab/show/Lance+Dixon">Lance Dixon</a>, <a class="existingWikiWord" href="/nlab/show/David+Kosower">David Kosower</a>, On-Shell Methods in Perturbative QCD (<a href="http://arxiv.org/abs/0704.2798">arXiv:0704.2798</a>)</li> </ul> See also <ul> <li> Bo-Lun Du, Xing-Gang Wu, Jian-Ming Shen, Stanley J. Brodsky, Extending the Predictive Power of Perturbative QCD (<a href="https://arxiv.org/abs/1807.11144">arXiv:1807.11144</a>) </li> <li> Christian Drischler, Wick Haxton, Kenneth McElvain, Emanuele Mereghetti, Amy Nicholson, Pavlos Vranas, André Walker-Loud, Towards grounding nuclear physics in QCD (<a href="https://arxiv.org/abs/1910.07961">arxiv:1910.07961</a>) </li> <li> George Savvidy: Landscape of QCD Vacuum [<a href="https://arxiv.org/abs/2407.00318">arXiv:2407.00318</a>] </li> </ul> As <a class="existingWikiWord" href="/nlab/show/thermal+field+theory">thermal field theory</a>: <ul> <li>Jacopo Ghiglieri, Aleksi Kurkela, Michael Strickland, Aleksi Vuorinen, Perturbative Thermal QCD: Formalism and Applications (<a href="https://arxiv.org/abs/2002.10188">arXiv:2002.10188</a>)</li> </ul> <h3 id="Phases">Phase diagram</h3> On the <a class="existingWikiWord" href="/nlab/show/phase+diagram">phase diagram</a> of <a class="existingWikiWord" href="/nlab/show/QCD">QCD</a>: <ul> <li id="Shuryak96"> <a class="existingWikiWord" href="/nlab/show/Edward+Shuryak">Edward Shuryak</a>, The Phases of QCD (<a href="https://arxiv.org/abs/hep-ph/9609249">arXiv:hep-ph/9609249</a>) </li> <li id="Hands01"> Simon Hands, The Phase Diagram of QCD, Contemp. Phys. 42:209-225, 2001 (<a href="https://arxiv.org/abs/physics/0105022">arXiv:physics/0105022</a>) </li> <li id="Schaefer05"> <a class="existingWikiWord" href="/nlab/show/Thomas+Schaefer">Thomas Schaefer</a>, Phases of QCD (<a href="https://arxiv.org/abs/hep-ph/0509068">arXiv:hep-ph/0509068</a>) </li> </ul> Via <a class="existingWikiWord" href="/nlab/show/lattice+QCD">lattice QCD</a>: <ul> <li>Jana N. Guenther, Overview of the QCD phase diagram – Recent progress from the lattice (<a href="https://arxiv.org/abs/2010.15503">arXiv:2010.15503</a>)</li> </ul> <h3 id="history">History</h3> On the early history of the development of quantum chromodynamics (the <a class="existingWikiWord" href="/nlab/show/quark">quark</a>-model): <ul> <li> <a class="existingWikiWord" href="/nlab/show/George+Zweig">George Zweig</a>, Origins of the quark model, 1980 (<a href="https://authors.library.caltech.edu/18969/1/Origins_of_the_Quark_Model_Final_Zweig%5B1%5D.pdf">pdf</a>, <a class="existingWikiWord" href="/nlab/files/ZweigQuarkModel1980.pdf" title="pdf">pdf</a>) </li> <li> <a class="existingWikiWord" href="/nlab/show/Mikhail+Shifman">Mikhail Shifman</a>, OPE-based Methods in Nonperturbative QCD, Eur. Phys. J. C (2022) [<a href="https://arxiv.org/abs/2208.10600">arXiv:2208.10600</a>] </li> </ul> See also: <ul> <li>Stefano Forte: Asymptotic Freedom in Parton Language: the Birth of Perturbative QCD [<a href="https://arxiv.org/abs/2501.13158">arXiv:2501.13158</a>]</li> </ul> <h3 id="lattice_qcd">Lattice QCD</h3> Due to <a class="existingWikiWord" href="/nlab/show/confinement">confinement</a>, the fundamental degrees of freedom in terms of which QCD is formulated, namely the <a class="existingWikiWord" href="/nlab/show/quarks">quarks</a>, are actually not the low-energy <a class="existingWikiWord" href="/nlab/show/bound+states">bound states</a> of the theory, which instead are the <a class="existingWikiWord" href="/nlab/show/hadrons">hadrons</a>. This leaves room to speculate that QCD is not really the fundamental theory of the <a class="existingWikiWord" href="/nlab/show/strong+nuclear+force">strong nuclear force</a>. However, brute-force computation in <a class="existingWikiWord" href="/nlab/show/lattice+QCD">lattice QCD</a> shows that the <a class="existingWikiWord" href="/nlab/show/quark">quark</a>-model does reproduce these <a class="existingWikiWord" href="/nlab/show/hadron">hadron</a> <a class="existingWikiWord" href="/nlab/show/bound+states">bound states</a> somehow (even if the real understanding of how it does so remains open, this is the <a class="existingWikiWord" href="/nlab/show/mass+gap+problem">mass gap problem</a>): <ul> <li> S. Durr, Z. Fodor, J. Frison, C. Hoelbling, R. Hoffmann, S.D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K.K. Szabo, G. Vulvert, Ab-initio Determination of Light Hadron Masses, Science 322:1224-1227,2008 (<a href="https://arxiv.org/abs/0906.3599">arXiv:0906.3599</a>) conclusion on p. 4: </li> </ul> <blockquote> our study strongly suggests that <a class="existingWikiWord" href="/nlab/show/QCD">QCD</a> is the theory of the <a class="existingWikiWord" href="/nlab/show/strong+nuclear+force">strong interaction</a>, at low energies as well </blockquote> <ul> <li id="FodorHoelbling12"> Zoltan Fodor, Christian Hoelbling, Light Hadron Masses from Lattice QCD, Rev. Mod. Phys. 84, 449, (<a href="https://arxiv.org/abs/1203.4789">arXiv:1203.4789</a>) </li> <li> S. Aoki et. al. Review of lattice results concerning low-energy particle physics (<a href="https://arxiv.org/abs/1607.00299">arXiv:1607.00299</a>) </li> </ul> On <a class="existingWikiWord" href="/nlab/show/string+diagram">string diagram</a>-calculus (<a href="string+diagram#Cvitanovic08">Cvitanović 2008</a>: “bird tracks”) for the <a class="existingWikiWord" href="/nlab/show/representation+theory">representation theory</a> involved in <a class="existingWikiWord" href="/nlab/show/quantum+chromodynamics">quantum chromodynamics</a> <ul> <li><a class="existingWikiWord" href="/nlab/show/St%C3%A9phane+Peign%C3%A9">Stéphane Peigné</a>, Introduction to color in QCD: Initiation to the birdtrack pictorial technique [<a href="https://arxiv.org/abs/2302.07574">arXiv:2302.07574</a>]</li> </ul> <h3 id="lightcone_quantization">Light-cone quantization</h3> Non-perturbative QCD and <a class="existingWikiWord" href="/nlab/show/hadron">hadron</a> bound states by <a class="existingWikiWord" href="/nlab/show/light-cone+quantization">light-cone quantization</a> (see there for more): <ul> <li> <a class="existingWikiWord" href="/nlab/show/G.+Peter+Lepage">G. Peter Lepage</a>, <a class="existingWikiWord" href="/nlab/show/Stanley+J.+Brodsky">Stanley J. Brodsky</a>, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22 (1980) 2157 [<a href="https://doi.org/10.1103/PhysRevD.22.2157">doi:10.1103/PhysRevD.22.2157</a>] </li> <li id="PauliBrodsky85b"> <a class="existingWikiWord" href="/nlab/show/Hans-Christian+Pauli">Hans-Christian Pauli</a>, <a class="existingWikiWord" href="/nlab/show/Stanley+J.+Brodsky">Stanley J. Brodsky</a>, Discretized light-cone quantization: Solution to a field theory in one space and one time dimension, Phys. Rev. D 32 (1985) 2001 [<a href="https://doi.org/10.1103/PhysRevD.32.2001">doi:10.1103/PhysRevD.32.2001</a>] </li> <li> <a class="existingWikiWord" href="/nlab/show/Stanley+J.+Brodsky">Stanley J. Brodsky</a>, Gary McCartor, <a class="existingWikiWord" href="/nlab/show/Hans-Christian+Pauli">Hans-Christian Pauli</a>, <a class="existingWikiWord" href="/nlab/show/Stephen+S.+Pinsky">Stephen S. Pinsky</a>, The challenge of light-cone quantization of gauge field theory, Particle World 3 3 (1993) 109-124 [<a href="http://cds.cern.ch/record/240388">cds:240388</a>, <a href="https://inspirehep.net/literature/335247">inspire:335247</a>] </li> <li id="BrodskyPauliPinsky98"> <a class="existingWikiWord" href="/nlab/show/Stanley+Brodsky">Stanley Brodsky</a>, <a class="existingWikiWord" href="/nlab/show/Hans-Christian+Pauli">Hans-Christian Pauli</a>, <a class="existingWikiWord" href="/nlab/show/Stephen+S.+Pinsky">Stephen S. Pinsky</a>, Quantum Chromodynamics and Other Field Theories on the Light Cone, Phys. Rept. 301 (1998) 299-486 [<a href="https://arxiv.org/abs/hep-ph/9705477">arXiv:hep-ph/9705477</a>, <a href="https://doi.org/10.1016/S0370-1573(97)00089-6">doi:10.1016/S0370-1573(97)00089-6</a>] </li> <li> <a class="existingWikiWord" href="/nlab/show/Stanley+Brodsky">Stanley Brodsky</a>, <a class="existingWikiWord" href="/nlab/show/Thomas+Heinzl">Thomas Heinzl</a> et al. Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physics, White Paper of International Light Cone Advisory Committee, Nuclear Physics B - Proceedings Supplements 251, 252 (2014) 165-174 [<a href="https://doi.org/10.1016/j.nuclphysbps.2014.05.004">doi:10.1016/j.nuclphysbps.2014.05.004</a>, <a href="https://arxiv.org/abs/1309.6333">arXiv:1309.6333</a>] </li> </ul> </body></html> </div> <div class="revisedby"> Last revised on January 31, 2025 at 04:42:44. 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