Nontrivial path integrals for nonrenormalizable fields—Multicomponent ultralocal models

Abstract

A nontrivial lattice-space path integral formulation of nonrenormalizable multicomponent ultralocal models is constructed from the nonperturbative operator solutions presented in a recent paper. The indefinite, nonclassical, singular potential required for the nontriviality has different effects on distributions compared to the single-component case, however, the essential property of reweighting the distribution at the origin is similar. The appearance of additional nonclassical, singular potentials suggests that we cannot always place the classical Lagrangian or classical Hamiltonian directly into the path-integral formulation, or in other words, a straightforward canonical quantization of fields with infinite degrees of freedom does not always apply.