Vacuum expectation value

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 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.
  • 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.
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