Quantum field theory
Feynman diagram
History
Background Field theory Electromagnetism Weak force Strong force Quantum mechanics Special relativity General relativity Gauge theory Yang–Mills theory
Symmetries Symmetry in quantum mechanics C-symmetry P-symmetry T-symmetry Lorentz symmetry Poincaré symmetry Gauge symmetry Explicit symmetry breaking Spontaneous symmetry breaking Noether charge Topological charge
Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation value Feynman diagram Lattice field theory LSZ reduction formula Partition function Propagator Quantization Regularization Renormalization Vacuum state Wick's theorem
Equations Dirac equation Klein–Gordon equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations
Standard Model Quantum electrodynamics Electroweak interaction Quantum chromodynamics Higgs mechanism
Incomplete theories String theory Supersymmetry Technicolor Theory of everything Quantum gravity
Scientists Adler Anderson Anselm Bargmann Becchi Belavin Bell Berezin Bethe Bjorken Bleuer Bogoliubov Brodsky Brout Buchholz Cachazo Callan Coleman Dashen DeWitt Dirac Doplicher Dyson Englert Faddeev Fadin Fayet Fermi Feynman Fierz Fock Frampton Fritzsch Fröhlich Fredenhagen Furry Glashow Gelfand Gell-Mann Goldstone Gribov Gross Gupta Guralnik Haag Heisenberg Hepp Higgs Hagen 't Hooft Iliopoulos Ivanenko Jackiw Jona-Lasinio Jordan Jost Källén Kendall Kinoshita Klebanov Kontsevich Kuraev Landau Lee Lehmann Leutwyler Lipatov Łopuszański Low Lüders Maiani Majorana Maldacena Migdal Mills Møller Naimark Nambu Neveu Nishijima Oehme Oppenheimer Osterwalder Parisi Pauli Peskin Plefka Polyakov Pomeranchuk Popov Proca Rubakov Ruelle Salam Schrader Schwarz Schwinger Segal Seiberg Semenoff Shifman Shirkov Skyrme Sommerfield Stora Stueckelberg Sudarshan Symanzik Thirring Tomonaga Tyutin Vainshtein Veltman Virasoro Ward Weinberg Weisskopf Wentzel Wess Wetterich Weyl Wick Wightman Wigner Wilczek Wilson Witten Yang Yukawa Zamolodchikov Zamolodchikov Zee Zimmermann Zinn-Justin Zuber Zumino
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In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by ${\displaystyle \langle O\rangle .}$ One of the most widely used examples of an observable physical effect that results from the vacuum expectation value of an operator is the Casimir effect.

This concept is important for working with correlation functions in quantum field theory. It is also important in spontaneous symmetry breaking. Examples are:

• The Higgs field has a vacuum expectation value of 246 GeV.^[1] This nonzero value underlies the Higgs mechanism of the Standard Model. This value is given by ${\displaystyle v=1/{\sqrt ((\sqrt {2))G_{F}^{0))}=2M_{W}/g\approx 246.22\,{\rm {GeV))}$, where M_W is the mass of the W Boson, ${\displaystyle G_{F}^{0))$ the reduced Fermi constant, and g the weak isospin coupling, in natural units. It is also near the limit of the most massive nuclei, at v = 264.3 Da.
• The chiral condensate in quantum chromodynamics, about a factor of a thousand smaller than the above, gives a large effective mass to quarks, and distinguishes between phases of quark matter. This underlies the bulk of the mass of most hadrons.
• The gluon condensate in quantum chromodynamics may also be partly responsible for masses of hadrons.

The observed Lorentz invariance of space-time allows only the formation of condensates which are Lorentz scalars and have vanishing charge.^{[citation needed]} Thus fermion condensates must be of the form ${\displaystyle \langle {\overline {\psi ))\psi \rangle }$, where ψ is the fermion field. Similarly a tensor field, G_μν, can only have a scalar expectation value such as ${\displaystyle \langle G_{\mu \nu }G^{\mu \nu }\rangle }$.

In some vacua of string theory, however, non-scalar condensates are found.^[which?] If these describe our universe, then Lorentz symmetry violation may be observable.