NONTRIVIAL PATH-INTEGRALS FOR NONRENORMALIZABLE FIELDS - MULTICOMPONENT ULTRALOCAL MODELS

A nontrivial lattice-space path integral formulation of nonrenormaliza ble multicomponent ultralocal models is constructed from the nonpertur bative operator solutions presented in a recent paper. The indefinite, nonclassical, singular potential required for the nontriviality has d ifferent effects on distributions compared to the single-component cas e, however, the essential property of reweighting the distribution at the origin is similar. The appearance of additional nonclassical, sing ular potentials suggests that we cannot always place the classical Lag rangian or classical Hamiltonian directly into the path-integral formu lation, or in other words, a straightforward canonical quantization of fields with infinite degrees of freedom does not always apply. (C) 19 95 American Institute of Physics.