The renormalizability for massive Abelian gauge field theories re-visited

TL;DR

This paper presents a simplified proof of the perturbative renormalizability of massive Abelian gauge theories, showing that gauge invariance and Stueckelberg's trick suffice without the Higgs mechanism or BRST analysis.

Contribution

It provides a streamlined proof of renormalizability for massive Abelian gauge theories using gauge invariance and Stueckelberg's trick, avoiding complex non-Abelian methods.

Findings

Massive Abelian gauge theories are perturbatively renormalizable.

No Higgs mechanism or BRST analysis is necessary for these theories.

The proof leverages Ward-Takahashi identities and gauge invariance.

Abstract

We give a simplified proof for the perturbative renormalizability of theories with massive vector particles. For renormalizability it is sufficient that the vector particle is treated as an gauge field, corresponding to an Abelian gauge group. Contrary to the non-Abelian case one does not need the Higgs mechanism to create the appropriate mass terms. The proof uses ``Stueckelberg's trick'' and the Ward-Takahashi identities from local Abelian gauge invariance. The simplification is due to the fact that, again contrary to the non-Abelian case, no BRST analysis is needed.