A canonical formalism of instantons and vacuum tunnelling in the (1+1)-dimensional Higgs model

Abstract

By taking as an example the (1+1)-dimensional Higgs model, we present a quantum field theory of instantons and vacuum tunnelling within the canonical formalism. To account for the nonperturbative nature of instantons, we make use of automorphisms of canonical commutation relation algebra. First, by postulating asymptotic completeness, we construct a series of inequivalent vacuum representations in the covariant gauge. Next, we construct a family of time-t representations which yield vacuum representations inequivalent to each other ast→±∞. The existence of such representations is shown to imply that the Fock vacuum undergoes tunnelling and hence is not the true vacuum of the theory. Thus the requirement of asymptotic completeness breaks down in the presence of instantons. We conclude that the physical space of the (1+1)-dimensional Higgs model corresponds to a direct sum of all the inequivalent gauge copies of the asymptotic Fock space.