A New Approach to Nonrenormalizable Models

TL;DR

This paper proposes a novel formulation for nonrenormalizable quantum field theories, focusing on ground-state distributions to demonstrate inherent nontriviality, challenging the standard renormalization approach.

Contribution

It introduces a new approach to nonrenormalizable models by emphasizing ground-state distributions, avoiding inappropriate counterterms, and addressing triviality issues.

Findings

Ground-state distribution functions can exhibit nontriviality from the start.

Conditions for bounds on correlation functions are derived.

Discussion on continuum limit issues is included.

Abstract

Nonrenormalizable quantum field theories require counterterms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counterterms suggested by renormalized perturbation theory are in fact inappropriate for this purpose. Guided by the potential underlying causes of triviality of such models, as obtained by alternative analyses, we focus attention on the ground-state distribution function, and suggest a formulation of such distributions that exhibits nontriviality from the start. Primary discussion is focused on self-interacting scalar fields. Conditions for bounds on general correlation functions are derived, and there is some discussion of the issues involved with the continuum limit.