Rethinking Renormalization

TL;DR

This paper proposes an enhanced renormalization approach to control nonrenormalizable quantum models, introducing new principles based on soluble examples and a recognition of interaction behavior, with implications for scalar quantum field theories.

Contribution

It introduces a novel renormalization framework that extends control to nonrenormalizable models using new principles and insights from soluble examples.

Findings

Developed a new renormalization scheme for nonrenormalizable models.

Identified a 'hard-core' behavior in interactions that aids in divergence removal.

Provided a background for a nontrivial quantization of scalar quantum fields.

Abstract

As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is proposed that is designed to bring the `nonrenormalizable models' under control as well. The new principles are developed by studying several, carefully chosen, soluble examples, and include a recognition of a `hard-core' behavior of the interaction and, in special cases, an extremely elementary procedure to remove the source of all divergences. Our discussion provides the background for a recent proposal for a nontrivial quantization of nonrenormalizable scalar quantum field models, which is briefly summarized as well.