# Vacuum expectation value

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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 ${\displaystyle \langle O\rangle .}$ 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 ${\displaystyle v=1/{\sqrt {{\sqrt {2}}G_{F}^{0}}}=2M_{W}/g\approx 246.22\,{\rm {GeV}}}$, where MW is the mass of the W Boson, ${\displaystyle G_{F}^{0}}$ the reduced Fermi constant, and g the weak isospin coupling, in natural units.

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, Gμν, 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.