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 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 This nonzero value underlies the
Higgs mechanism of the Standard Model. This
value is given by
v
=
1
/
2
G
F
0
=
2
M
W
/
g
≈
246.22
G
e
V
{\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,
G
F
0
{\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. 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, Gμν, can only have a scalar
expectation value such as
⟨
G
μ
ν
G
μ
ν
⟩
{\displaystyle \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
