Modified Proca theory in arbitrary and two dimensions

Abstract

We demonstrate that the standard St{$\ddot u$}ckelberg-modified Proca theory (i.e. a massive Abelian 1-form theory) respects the classical gauge and corresponding quantum (anti-)BRST symmetry transformations in any arbitrary dimension of spacetime within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We further show that the St{$\ddot u$}ckelberg formalism gets modified in the two (1+1)-dimensions of spacetime due to a couple of discrete duality symmetry transformations in the theory which turn out to be responsible for the existence of the nilpotent (anti-)co-BRST symmetry transformations corresponding to the nilpotent (anti-)BRST symmetry transformations of our theory. These nilpotent symmetries exist together in the modified version of the two (1+1)-dimensional (2D) Proca theory. We provide the mathematical basis for the modification of the St{$\ddot u$}ckelberg-technique, the existence of the discrete duality as well as the continuous (anti-)co-BRST symmetry transformations in the 2D modified version of Proca theory.