Vacuum expectation value

Quantum field theory
(Feynman diagram)
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Background Field theory Gauge theory Poincaré symmetry Quantum mechanics Spontaneous symmetry breaking
Symmetries Charge conjugation Crossing Parity Time reversal
Tools Anomaly Effective field theory Expectation value Faddeev–Popov ghosts Feynman diagram Lattice gauge theory LSZ reduction formula Partition function Propagator Quantization Renormalization Vacuum state Wick's theorem Wightman axioms
Equations Dirac equation Klein–Gordon equation Proca equations Wheeler–DeWitt equation
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Scientists Adler Bethe Bogoliubov Callan Candlin Coleman DeWitt Dirac Dyson Fermi Feynman Fierz Fröhlich Gell-Mann Goldstone Gross 't Hooft Jackiw Klein Landau Lee Lehmann Majorana Nambu Parisi Polyakov Salam Schwinger Skyrme Stueckelberg Symanzik Tomonaga Veltman Weinberg Weisskopf Wilson Witten Yang Yukawa Hoodbhoy Zimmermann Zinn-Justin

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 $\langle O\rangle$. One of the best known 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. This nonzero value allows the Higgs mechanism to work.
• The chiral condensate in Quantum chromodynamics gives a large effective mass to quarks, and distinguishes between phases of quark matter.
• The gluon condensate in Quantum chromodynamics may 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. Thus fermion condensates must be of the form $\langle\overline\psi\psi\rangle$, where ψ is the fermion field. Similarly a tensor field, G_μν, can only have a scalar expectation value such as $\langle G_{\mu\nu}G^{\mu\nu}\rangle$.

In some vacua of string theory, however, non-scalar condensates are found. 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