Reducible Stueckelberg symmetry and dualities

TL;DR

This paper introduces a method for incorporating reducible Stueckelberg gauge symmetries into theories, exemplified by the Proca model, revealing dual formulations and different gauge fixing options.

Contribution

It develops a general iterative procedure for including reducible Stueckelberg fields, expanding the understanding of gauge symmetries and dualities in field theories.

Findings

The procedure applies to the Proca model with a third order involutive closure.

Different gauge fixings lead to equivalent or dual formulations of the original theory.

The approach suggests similar dualities for fields of various spins.

Abstract

We propose a general procedure for iterative inclusion of Stueckelberg fields to convert the theory into gauge system being equivalent to the original one. In so doing, we admit reducibility of the Stueckelberg gauge symmetry. In this case, no pairing exists between Stueckelberg fields and gauge parameters, unlike the irreducible Stueckelberg symmetry. The general procedure is exemplified by the case of Proca model, with the third order involutive closure chosen as the starting point. In this case, the set of Stueckelberg fields includes, besides the scalar, also the second rank antisymmetric tensor. The reducible Stueckelberg gauge symmetry is shown to admit different gauge fixing conditions. One of the gauges reproduces the original Proca theory, while another one excludes the original vector and the Stueckelberg scalar. In this gauge, the irreducible massive spin one is represented by antisymmetric second rank tensor obeying the third order field equations. Similar dual formulations are expected to exist for the fields of various spins.