Vacuum expectation value

In quantum field theory, the Template:W (VEV) of an Template:W is the operator's average (or Template:W) in the vacuum (i.e. in the Template:W). When explaining the concept of a VEV, physicists often cite the Template:W 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 $\mathrm{\Psi }$ by a Template:W of the form $\mathrm{\Phi }\bar{\mathrm{\Psi }}$$\mathrm{\Psi }$, then this vacuum expectation value would act like a Template:W 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, Template:Cite journal (quote from p. 30)

• A new conceptual foundation for Template:W T_μν on locally flat Template:W—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 Template:W is taken. The same ideas allow us to treat, for the first time, self-interacting fields for arbitrary mass in Template:W—using traditional flat-space-time renormalization theory. First-order results for zero-mass λφ⁴ theory agree with those recently announced by Template:W. We point out the crucial role played by the simple renormalization condition that the vacuum expectation value of T_μν must vanish in Minkowski space-time, and in a critical discussion of other approaches, we clarify the question of renormalization ambiguities for T_μν in curved space-times.
  • Bernard S. Kay Template:Cite journal

• Vacuum expectation values of products of neutral Template:W operators are discussed. The properties of these distributions arising from Template:W, the absence of Template:W states and the Template:W of the scalar product are determined. The vacuum expectation values are shown to be Template:Ws of Template:Ws. 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, Template:Cite journal