Gauge invariance in gravity-like descriptions of massive gauge field theories

TL;DR

This paper explores gravity-like formulations of massive gauge theories, focusing on gauge invariance, alternative tensor-based descriptions, and the well-defined massless limit in antisymmetric tensor formulations.

Contribution

It introduces gravity-like descriptions of massive gauge theories using antisymmetric tensors and geometric variables, clarifying gauge invariance and massless limits.

Findings

Stückelberg degrees of freedom factor out in both approaches

Massless limit exists for antisymmetric tensor fields but not in vector potential formulation

Alternative descriptions provide new insights into gauge invariance

Abstract

We discuss gravity-like formulations of massive Abelian and non-Abelian gauge field theories in four space-time dimensions with particular emphasis on the issue of gauge invariance. Alternative descriptions in terms of antisymmetric tensor fields and geometric variables, respectively, are analysed. In both approaches St\"uckelberg degrees of freedom factor out. We also demonstrate, in the Abelian case, that the massless limit for the gauge propagator, which does not exist in the vector potential formulation, is well-defined for the antisymmetric tensor fields.