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Quantum field theory
Feynman diagram
History
Background Field theory Electromagnetism Weak force Strong force Quantum mechanics Special relativity General relativity Gauge theory
Symmetries Symmetry in quantum mechanics C-symmetry P-symmetry T-symmetry Space translation symmetry Time translation symmetry Rotation symmetry Lorentz symmetry Poincaré symmetry Gauge symmetry Explicit symmetry breaking Spontaneous symmetry breaking Yang–Mills theory Noether charge Topological charge
Tools Anomaly Crossing Effective field theory Expectation value Ghost fields Faddeev–Popov ghosts Feynman diagram Lattice gauge theory LSZ reduction formula Partition function Propagator Quantization Regularization Renormalization Vacuum state Wick's theorem Wightman axioms Feynman parametrization
Equations Dirac equation Klein–Gordon equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations Joos–Weinberg equation Weyl equation
Standard Model Quantum electrodynamics Electroweak interaction Quantum chromodynamics Higgs mechanism
Incomplete theories Topological quantum field theory String theory Superstring theory M-Theory Supersymmetry Supergravity Technicolor Theory of everything Quantum gravity
Scientists C. D. Anderson P. W. Anderson Bethe Bjorken Bogoliubov Brout Callan Coleman DeWitt Dirac Dyson Englert Fermi Feynman Fierz Fock Fröhlich Glashow Gell-Mann Gross Guralnik Heisenberg Higgs Haag Hagen 't Hooft Jordan Kendall Kibble Lamb Landau Lee Majorana Mills Nambu Nishijima Parisi Polyakov Salam Schwinger Skyrme Sudarshan Tomonaga Veltman Ward Weinberg Weisskopf Weyl Wilczek Wilson Yang Yukawa
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In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by ⟨O⟩.{displaystyle langle Orangle .} One of the most widely used, but controversial, 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 v=1/2GF0=2MW/g≈246.22GeV{displaystyle v=1/{sqrt {{sqrt {2}}G_{F}^{0}}}=2M_{W}/gapprox 246.22,{rm {GeV}}}, where M_W is the mass of the W Boson, GF0{displaystyle G_{F}^{0}} the reduced Fermi constant, and g the weak isospin coupling, in natural units.

• 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 ⟨ψ¯ψ⟩{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 ⟨GμνGμν⟩{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.

See also

• 
  Wightman axioms and Correlation function (quantum field theory)
  


• 
  vacuum energy or dark energy
  


• Spontaneous symmetry breaking

References

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