Taming Nonrenormalizability

TL;DR

This paper proposes a pseudofree model for relativistic nonrenormalizable scalar fields, suggesting that their interaction acts as a hard core, leading to divergence-free perturbation expansions and a new understanding of their continuum limits.

Contribution

It introduces a pseudofree model for nonrenormalizable quantum field theories, providing a framework where perturbation expansions are divergence-free and the models are connected to a pseudofree theory.

Findings

Pseudofree models account for hard core interactions in nonrenormalizable theories.

Perturbation expansions about the pseudofree model are divergence-free.

Supports the idea that nonrenormalizable models are connected to a pseudofree theory.

Abstract

Nonrenormalizable scalar fields, such as \varphi^4_n, n\ge5, require infinitely many distinct counter terms when perturbed about the free theory, and lead to free theories when defined as the continuum limit of a lattice regularized theory restricted only to arbitrary mass and coupling constant renormalization. Based on the proposal that functional integrals for interacting nonrenormalizable models do not reduce to the expression for the free field functional integral as the coupling constant vanishes -- a proposal supported by the fact that even the set of classical solutions for such models does not reduce to the set of free field solutions as the coupling constant vanishes -- it has been conjectured that for nonrenormalizable models the interaction term acts partially as a hard core eliminating certain fields otherwise allowed by the free theory. As a consequence, interacting models are continuously connected to a pseudofree theory that takes into account the hard core as the coupling constant vanishes, and this general view is supported not only by simple quantum mechanical examples as well as soluble but nonrelativistic nonrenormalizable models. The present article proposes a pseudofree model for relativistic nonrenormalizable models about which it is argued that a perturbation expansion of the interaction is term-by-term divergence free.