On the equivalence between topologically and non-topologically massive abelian gauge theories

TL;DR

This paper demonstrates the equivalence between topologically massive gauge theories and various non-topologically massive formulations in the canonical framework, revealing they differ only by total divergence terms.

Contribution

It establishes a canonical equivalence between TMGT and multiple NTMGT formulations, including St"uckelberg, Proca, and Kalb-Ramond theories, with covariant mappings of fields.

Findings

Different NTMGTs are equivalent to different TMGT formulations.

The Hamiltonian maps between theories under canonical transformations.

Covariant field mappings relate TMGT and NTMGT correlation functions.

Abstract

We analyse the equivalence between topologically massive gauge theory (TMGT) and different formulations of non-topologically massive gauge theories (NTMGTs) in the canonical approach. The different NTMGTs studied are St\"uckelberg formulation of (A) a first order formulation involving one and two form fields, (B) Proca theory, and (C) massive Kalb-Ramond theory. We first quantise these reducible gauge systems by using the phase space extension procedure and using it, identify the phase space variables of NTMGTs which are equivalent to the canonical variables of TMGT and show that under this the Hamiltonian also get mapped. Interestingly it is found that the different NTMGTs are equivalent to different formulations of TMGTs which differ only by a total divergence term. We also provide covariant mappings between the fields in TMGT to NTMGTs at the level of correlation function.