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vacuum diagram in nLab
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function() { generateThmNumbers(); }); </script> </head> <body> <div id="Container"> <div id="Content"> <h1 id="pageName"> <span style="float: left; margin: 0.5em 0.25em -0.25em 0"> <svg xmlns="http://www.w3.org/2000/svg" width="1.872em" height="1.8em" viewBox="0 0 190 181"> <path fill="#226622" d="M72.8 145c-1.6 17.3-15.7 10-23.6 20.2-5.6 7.3 4.8 15 11.4 15 11.5-.2 19-13.4 26.4-20.3 3.3-3 8.2-4 11.2-7.2a14 14 0 0 0 2.9-11.1c-1.4-9.6-12.4-18.6-16.9-27.2-5-9.6-10.7-27.4-24.1-27.7-17.4-.3-.4 26 4.7 30.7 2.4 2.3 5.4 4.1 7.3 6.9 1.6 2.3 2.1 5.8-1 7.2-5.9 2.6-12.4-6.3-15.5-10-8.8-10.6-15.5-23-26.2-31.8-5.2-4.3-11.8-8-18-3.7-7.3 4.9-4.2 12.9.2 18.5a81 81 0 0 0 30.7 23c3.3 1.5 12.8 5.6 10 10.7-2.5 5.2-11.7 3-15.6 1.1-8.4-3.8-24.3-21.3-34.4-13.7-3.5 2.6-2.3 7.6-1.2 11.1 2.8 9 12.2 17.2 20.9 20.5 17.3 6.7 34.3-8 50.8-12.1z"/> <path fill="#a41e32" d="M145.9 121.3c-.2-7.5 0-19.6-4.5-26-5.4-7.5-12.9-1-14.1 5.8-1.4 7.8 2.7 14.1 4.8 21.3 3.4 12 5.8 29-.8 40.1-3.6-6.7-5.2-13-7-20.4-2.1-8.2-12.8-13.2-15.1-1.9-2 9.7 9 21.2 12 30.1 1.2 4 2 8.8 6.4 10.3 6.9 2.3 13.3-4.7 17.7-8.8 12.2-11.5 36.6-20.7 43.4-36.4 6.7-15.7-13.7-14-21.3-7.2-9.1 8-11.9 20.5-23.6 25.1 7.5-23.7 31.8-37.6 38.4-61.4 2-7.3-.8-29.6-13-19.8-14.5 11.6-6.6 37.6-23.3 49.2z"/> <path fill="#193c78" d="M86.3 47.5c0-13-10.2-27.6-5.8-40.4 2.8-8.4 14.1-10.1 17-1 3.8 11.6-.3 26.3-1.8 38 11.7-.7 10.5-16 14.8-24.3 2.1-4.2 5.7-9.1 11-6.7 6 2.7 7.4 9.2 6.6 15.1-2.2 14-12.2 18.8-22.4 27-3.4 2.7-8 6.6-5.9 11.6 2 4.4 7 4.5 10.7 2.8 7.4-3.3 13.4-16.5 21.7-16 14.6.7 12 21.9.9 26.2-5 1.9-10.2 2.3-15.2 3.9-5.8 1.8-9.4 8.7-15.7 8.9-6.1.1-9-6.9-14.3-9-14.4-6-33.3-2-44.7-14.7-3.7-4.2-9.6-12-4.9-17.4 9.3-10.7 28 7.2 35.7 12 2 1.1 11 6.9 11.4 1.1.4-5.2-10-8.2-13.5-10-11.1-5.2-30-15.3-35-27.3-2.5-6 2.8-13.8 9.4-13.6 6.9.2 13.4 7 17.5 12C70.9 34 75 43.8 86.3 47.4z"/> </svg> </span> <span class="webName">nLab</span> vacuum diagram </h1> <div class='rightHandSide'> <div class='toc clickDown' tabindex='0'> <h3 id='context'>Context</h3> <h4 id='vacua'>Vacua</h4> <div class='hide'> <p><strong><a class='existingWikiWord' href='/nlab/show/vacuum'>vacuum</a></strong></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/vacuum+state'>vacuum state</a>, <a class='existingWikiWord' href='/nlab/show/Hadamard+distribution'>Hadamard state</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/interacting+vacuum'>interacting vacuum</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/vacuum+expectation+value'>vacuum expectation value</a>, <a class='existingWikiWord' href='/nlab/show/vacuum+amplitude'>vacuum amplitude</a>, <a class='existingWikiWord' href='/nlab/show/quantum+fluctuation'>vacuum fluctuation</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/vacuum+energy'>vacuum energy</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/KMS+state'>thermal vacuum</a>, <a class='existingWikiWord' href='/nlab/show/KMS+state'>KMS state</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/vacuum+diagram'>vacuum diagram</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/vacuum+stability'>vacuum stability</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/false+vacuum'>false vacuum</a>, <a class='existingWikiWord' href='/nlab/show/tachyon'>tachyon</a>, <a class='existingWikiWord' href='/nlab/show/Coleman-De+Luccia+instanton'>Coleman-De Luccia instanton</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/theta+vacuum'>theta vacuum</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/perturbative+string+theory+vacuum'>perturbative string theory vacuum</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/non-geometric+string+vacuum'>non-geometric string theory vacuum</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/landscape+of+string+theory+vacua'>landscape of string theory vacua</a></p> </li> </ul> </li> </ul> </div> <h4 id='algebraic_quantum_field_theory'>Algebraic Quantum Field Theory</h4> <div class='hide'> <p><strong><a class='existingWikiWord' href='/nlab/show/AQFT'>algebraic quantum field theory</a></strong> (<a class='existingWikiWord' href='/nlab/show/perturbative+algebraic+quantum+field+theory'>perturbative</a>, <a class='existingWikiWord' href='/nlab/show/AQFT+on+curved+spacetimes'>on curved spacetimes</a>, <a class='existingWikiWord' href='/nlab/show/homotopical+algebraic+quantum+field+theory'>homotopical</a>)</p> <p><a class='existingWikiWord' href='/nlab/show/geometry+of+physics+--+perturbative+quantum+field+theory'>Introduction</a></p> <h2 id='concepts'>Concepts</h2> <p><strong><a class='existingWikiWord' href='/nlab/show/field+theory'>field theory</a></strong>:</p> <ul> <li> <p><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></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/relativistic+quantum+field+theory'>relativistic</a>, <a class='existingWikiWord' href='/nlab/show/Euclidean+field+theory'>Euclidean</a>, <a class='existingWikiWord' href='/nlab/show/Euclidean+field+theory'>thermal</a></p> </li> </ul> <p><strong><a class='existingWikiWord' href='/nlab/show/Lagrangian+quantum+field+theory'>Lagrangian field theory</a></strong></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/field+%28physics%29'>field (physics)</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/field+bundle'>field bundle</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/field+history'>field history</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/space+of+field+histories'>space of field histories</a></p> </li> </ul> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Lagrangian+density'>Lagrangian density</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/Euler-Lagrange+form'>Euler-Lagrange form</a>, <a class='existingWikiWord' href='/nlab/show/pre-symplectic+current'>presymplectic current</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Euler-Lagrange+equation'>Euler-Lagrange</a> <a class='existingWikiWord' href='/nlab/show/Euler-Lagrange+equation'>equations of motion</a></p> </li> </ul> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/locally+variational+field+theory'>locally variational field theory</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/phase+space'>covariant phase space</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/Peierls+bracket'>Peierls-Poisson bracket</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/advanced+and+retarded+causal+propagators'>advanced and retarded propagator</a>,</p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/causal+propagator'>causal propagator</a></p> </li> </ul> </li> </ul> </li> </ul> <p><strong><a class='existingWikiWord' href='/nlab/show/quantization'>quantization</a></strong></p> <ul> <li> <p><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></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/formal+deformation+quantization'>algebraic deformation quantization</a>, <a class='existingWikiWord' href='/nlab/show/star-algebra'>star algebra</a></p> </li> </ul> <p><strong><a class='existingWikiWord' href='/nlab/show/quantum+mechanics'>quantum mechanical system</a></strong>, <strong><a class='existingWikiWord' href='/nlab/show/quantum+probability+theory'>quantum probability</a></strong></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/subsystem'>subsystem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/observable'>observables</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/field+observable'>field observables</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/local+observable'>local observables</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/polynomial+observable'>polynomial observables</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/microcausal+polynomial+observable'>microcausal observables</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/operator+algebra'>operator algebra</a>, <a class='existingWikiWord' href='/nlab/show/C-star-algebra'>C*-algebra</a>, <a class='existingWikiWord' href='/nlab/show/von+Neumann+algebra'>von Neumann algebra</a></p> </li> </ul> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/causally+local+net+of+observables'>local net of observables</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/causal+locality'>causal locality</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Haag-Kastler+axioms'>Haag-Kastler axioms</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Wightman+axioms'>Wightman axioms</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/field+net'>field net</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/conformal+net'>conformal net</a></p> </li> </ul> </li> <li> <p><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></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/pure+state'>pure state</a></p> <p><a class='existingWikiWord' href='/nlab/show/space+of+states+%28in+geometric+quantization%29'>wave function</a></p> <p><a class='existingWikiWord' href='/nlab/show/wave+function+collapse'>collapse of the wave function</a>/<a class='existingWikiWord' href='/nlab/show/conditional+expectation'>conditional expectation value</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/density+matrix'>mixed state</a>, <a class='existingWikiWord' href='/nlab/show/density+matrix'>density matrix</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/space+of+states+%28in+geometric+quantization%29'>space of quantum states</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/vacuum+state'>vacuum state</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/quasi-free+quantum+state'>quasi-free state</a>,</p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Hadamard+distribution'>Hadamard state</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Hadamard+distribution'>Wightman propagator</a></p> </li> </ul> </li> </ul> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/picture+of+mechanics'>picture of quantum mechanics</a></p> </li> </ul> <p><strong><a class='existingWikiWord' href='/nlab/show/free+field'>free field</a> <a class='existingWikiWord' href='/nlab/show/quantization'>quantization</a></strong></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/star-algebra'>star algebra</a>, <a class='existingWikiWord' href='/nlab/show/Moyal+deformation+quantization'>Moyal deformation quantization</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Wick+algebra'>Wick algebra</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/canonical+commutation+relation'>canonical commutation relations</a>, <a class='existingWikiWord' href='/nlab/show/Weyl+relation'>Weyl relations</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Wick+algebra'>normal ordered product</a></p> </li> </ul> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Fock+space'>Fock space</a></p> </li> </ul> <p><strong><a class='existingWikiWord' href='/nlab/show/gauge+theory'>gauge theories</a></strong></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/gauge+transformation'>gauge symmetry</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/BRST+complex'>BRST complex</a>, <a class='existingWikiWord' href='/nlab/show/BV-BRST+formalism'>BV-BRST formalism</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/local+BRST+cohomology'>local BV-BRST complex</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/BV-operator'>BV-operator</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/quantum+master+equation'>quantum master equation</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Ward+identity'>master Ward identity</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/quantum+anomaly'>gauge anomaly</a></p> </li> </ul> <p><strong><a class='existingWikiWord' href='/nlab/show/interacting+field+theory'>interacting field</a> <a class='existingWikiWord' href='/nlab/show/quantization'>quantization</a></strong></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/causal+perturbation+theory'>causal perturbation theory</a>, <a class='existingWikiWord' href='/nlab/show/perturbative+algebraic+quantum+field+theory'>perturbative AQFT</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/interaction'>interaction</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/S-matrix'>S-matrix</a>, <a class='existingWikiWord' href='/nlab/show/scattering+amplitude'>scattering amplitude</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/causal+additivity'>causal additivity</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/time-ordered+product'>time-ordered product</a>, <a class='existingWikiWord' href='/nlab/show/Feynman+propagator'>Feynman propagator</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Feynman+diagram'>Feynman diagram</a>, <a class='existingWikiWord' href='/nlab/show/S-matrix'>Feynman perturbation series</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/effective+action'>effective action</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/vacuum+stability'>vacuum stability</a></p> </li> </ul> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/interacting+field+algebra+of+observables'>interacting field algebra</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/Bogoliubov%27s+formula'>Bogoliubov's formula</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/M%C3%B8ller+operator'>quantum M酶ller operator</a></p> </li> </ul> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/adiabatic+switching'>adiabatic limit</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/infrared+divergence'>infrared divergence</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/interacting+vacuum'>interacting vacuum</a></p> </li> </ul> </li> </ul> <p><strong><a class='existingWikiWord' href='/nlab/show/renormalization'>renormalization</a></strong></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/renormalization+scheme'>("re-")normalization scheme</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/extension+of+distributions'>extension of distributions</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/renormalization+condition'>("re"-)normalization condition</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/quantum+anomaly'>quantum anomaly</a></p> </li> </ul> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/renormalization+group'>renormalization group</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/interaction+vertex+redefinition'>interaction vertex redefinition</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/St%C3%BCckelberg-Petermann+renormalization+group'>St眉ckelberg-Petermann renormalization group</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/renormalization+group+flow'>renormalization group flow</a>/<a class='existingWikiWord' href='/nlab/show/renormalization+group+flow'>running coupling constants</a></p> </li> </ul> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/effective+quantum+field+theory'>effective quantum field theory</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/effective+quantum+field+theory'>UV cutoff</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/counterterm'>counterterms</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/effective+action+functional'>relative effective action</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Polchinski%27s+flow+equation'>Wilsonian RG</a>, <a class='existingWikiWord' href='/nlab/show/Polchinski%27s+flow+equation'>Polchinski flow equation</a></p> </li> </ul> </li> </ul> <h2 id='Theorems'>Theorems</h2> <h3 id='states_and_observables'>States and observables</h3> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/order-theoretic+structure+in+quantum+mechanics'>order-theoretic structure in quantum mechanics</a></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/Alfsen-Shultz+theorem'>Alfsen-Shultz theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/D%C3%B6ring-Harding-Hamhalter+theorem'>Harding-D枚ring-Hamhalter theorem</a></p> </li> </ul> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Kochen-Specker+theorem'>Kochen-Specker theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Bell%27s+inequality'>Bell's theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Fell%27s+theorem'>Fell's theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Gleason%27s+theorem'>Gleason's theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Wigner+theorem'>Wigner theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Bub-Clifton+theorem'>Bub-Clifton theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Kadison-Singer+problem'>Kadison-Singer problem</a></p> </li> </ul> <h3 id='operator_algebra'>Operator algebra</h3> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/Wick%27s+lemma'>Wick's theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Gelfand-Naimark-Segal+construction'>GNS construction</a></p> <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> <p><a class='existingWikiWord' href='/nlab/show/modular+theory'>modular theory</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Fell%27s+theorem'>Fell's theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Stone-von+Neumann+theorem'>Stone-von Neumann theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Haag%27s+theorem'>Haag's theorem</a></p> </li> </ul> <h3 id='local_qft'>Local QFT</h3> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/Reeh-Schlieder+theorem'>Reeh-Schlieder theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Bisognano-Wichmann+theorem'>Bisognano-Wichmann theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/PCT+theorem'>PCT theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/spin-statistics+theorem'>spin-statistics theorem</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/DHR+superselection+theory'>DHR superselection theory</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/Osterwalder-Schrader+theorem'>Osterwalder-Schrader theorem</a> (<a class='existingWikiWord' href='/nlab/show/Wick+rotation'>Wick rotation</a>)</p> </li> </ul> <h3 id='perturbative_qft'>Perturbative QFT</h3> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/Schwinger-Dyson+equation'>Schwinger-Dyson equation</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/main+theorem+of+perturbative+renormalization'>main theorem of perturbative renormalization</a></p> </li> </ul> </div> </div> </div> <h1 id='contents'>Contents</h1> <div class='maruku_toc'><ul><li><a href='#idea'>Idea</a></li><li><a href='#related_concepts'>Related concepts</a></li></ul></div> <h2 id='idea'>Idea</h2> <p>A <a class='existingWikiWord' href='/nlab/show/Feynman+diagram'>Feynman diagram</a> without external edges is called a <em>vacuum diagram</em>.</p> <p>For example the simplest vacuum diagram obtained from the <a class='existingWikiWord' href='/nlab/show/electron-photon+interaction'>electron-photon interaction</a> in <a class='existingWikiWord' href='/nlab/show/quantum+electrodynamics'>quantum electrodynamics</a> is</p> <center> <img src='https://ncatlab.org/nlab/files/QEDVacuumDiagram.png' width='200'/> </center> <p>In the computation of <a class='existingWikiWord' href='/nlab/show/scattering+amplitude'>scattering amplitudes</a> in a <a class='existingWikiWord' href='/nlab/show/vacuum+stability'>stable vacuum</a> the contribution of the vacuum diagrams to the <a class='existingWikiWord' href='/nlab/show/S-matrix'>Feynman perturbation series</a> cancels out.</p> <p>For details see at <em><a class='existingWikiWord' href='/nlab/show/S-matrix'>S-matrix</a></em> <a href='S-matrix#VacuumDiagrams'>this section</a></p> <h2 id='related_concepts'>Related concepts</h2> <ul> <li> <p><strong><a class='existingWikiWord' href='/nlab/show/vacuum'>vacuum</a></strong></p> <ul> <li> <p><a class='existingWikiWord' href='/nlab/show/vacuum+state'>vacuum state</a>, <a class='existingWikiWord' href='/nlab/show/Hadamard+distribution'>Hadamard vacuum state</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/interacting+vacuum'>interacting vacuum</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/vacuum+expectation+value'>vacuum expectation value</a>, <a class='existingWikiWord' href='/nlab/show/vacuum+amplitude'>vacuum amplitude</a>, <a class='existingWikiWord' href='/nlab/show/quantum+fluctuation'>vacuum fluctuation</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/vacuum+energy'>vacuum energy</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/vacuum+stability'>vacuum stability</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/false+vacuum'>false vacuum</a>, <a class='existingWikiWord' href='/nlab/show/tachyon'>tachyon</a>, <a class='existingWikiWord' href='/nlab/show/Coleman-De+Luccia+instanton'>Coleman-De Luccia instanton</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/theta+vacuum'>theta vacuum</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/perturbative+string+theory+vacuum'>perturbative string theory vacuum</a></p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/landscape+of+string+theory+vacua'>landscape of string theory vacua</a></p> </li> </ul> </li> </ul> <p> </p> </div> <!-- Content --> </div> <!-- Container --> </body> </html>