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

We analyze the equivalence between topologically massive gauge theory (TMGT ) and different formulations of non-topologically massive gauge theories (N TMGTs) in the canonical approach. The different NTMGTs studied are Stuckelb erg formulation of (a) a first-order formulation involving one- and two-for m fields, (b) Proca theory, and (c) massive Kalb-Ramond theory. We first qu antize these reducible gauge systems by using the phase space extension pro cedure 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.