Vacuum expectation value

In quantum field theory, the   (VEV) of an is the operator's average (or ) in the vacuum (i.e. in the ). When explaining the concept of a VEV, physicists often cite the as an important example of an phenomenon resulting from the VEV of of an operator.

Quotes

 * I remember a lunch in which Schwinger began by saying to Weisskopf, “Now I will make you a world.” The “world” was written down on a few paper napkins, one of which I saved. In any event, one of the things that he said, which has stuck with me ever since, was that scalar particles were the only ones that could have nonvanishing vacuum expectation values. He then went on to say that if you couple one of these to a fermion $$\Psi$$ by a of the form $$\Phi \overline \Psi$$$$\Psi$$, then this vacuum expectation value would act like a  mass. This sort of coupling is how mass generation is done in principle for the fermions. All particles in this picture would acquire their masses from the vacuum.
 * Jeremy Bernstein, (quote from p. 30)


 * A new conceptual foundation for Tμν on locally flat —to obtain the so-called Casimir effect—is presented. The Casimir ground state is viewed locally as a (nonvacuum) state on Minkowski space-time and the expectation value of the normal-ordered  is taken. The same ideas allow us to treat, for the first time, self-interacting fields for arbitrary mass in —using traditional flat-space-time renormalization theory. First-order results for zero-mass λφ4 theory agree with those recently announced by . We point out the crucial role played by the simple renormalization condition that the vacuum expectation value of Tμν must vanish in Minkowski space-time, and in a critical discussion of other approaches, we clarify the question of renormalization ambiguities for Tμν in curved space-times.
 * Bernard S. Kay


 * Vacuum expectation values of products of neutral operators are discussed. The properties of these distributions arising from, the absence of  states and the  of the scalar product are determined. The vacuum expectation values are shown to be s of s. Local commutativity of the field is shown to be equivalent to a symmetry property of the analytic functions. The problem of determining a theory of a neutral scalar field given its vacuum expectation values is posed and solved.
 * Arthur Wightman,