Vacuum expectation value
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In quantum field theory the vacuum expectation value (also called condensate) of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by <math>\langle O\rangle<math>.
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 250 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 <math>\langle\overline\psi\psi\rangle<math>, where ψ is the fermion field. Similarly a tensor field, Gμν, can only have a scalar expectation value such as <math>\langle G_{\mu\nu}G^{\mu\nu}\rangle<math>.
In some vacua of string theory, however, non-scalar condensates are found. If these describe our universe, then Lorentz symmetry violation may be observable.