Renormalizability of Nonrenormalizable Field Theories

TL;DR

This paper demonstrates that certain nonrenormalizable field theories are physically equivalent to renormalizable ones by using the BRS formalism and the Equivalence Theorem, revealing a new perspective on their renormalizability.

Contribution

It provides a simple proof of the Equivalence Theorem and identifies a subclass of nonrenormalizable theories equivalent to renormalizable theories through cohomological analysis.

Findings

Nonrenormalizable theories can be equivalent to renormalizable ones.

The nonrenormalizable part acts like a gauge fixing.

Cohomological triviality explains the equivalence.

Abstract

We give a simple and elegant proof of the Equivalence Theorem, stating that two field theories related by nonlinear field transformations have the same S matrix. We are thus able to identify a subclass of nonrenormalizable field theories which are actually physically equivalent to renormalizable ones. Our strategy is to show by means of the BRS formalism that the "nonrenormalizable" part of such fake nonrenormalizable theories, is a kind of gauge fixing, being confined in the cohomologically trivial sector of the theory.