Gauge Invariances in the Proca model

TL;DR

This paper demonstrates how the gauge non-invariant Proca model can be transformed into gauge-invariant theories using the Gauge Unfixing method, preserving Lorentz invariance and producing multiple gauge theories.

Contribution

It introduces the Gauge Unfixing method to convert the Proca model into gauge theories with first class constraints, including the Stuckelberg and Maxwell-antisymmetric tensor theories.

Findings

Multiple gauge theories derived from the Proca model.

The method preserves Lorentz invariance.

Provides a systematic approach to gauge invariance.

Abstract

We show that the abelian Proca model, which is gauge non-invariant with second class constraints can be converted into gauge theories with first class constraints. The method used, which we call Gauge Unfixing employs a projection operator defined in the original phase space. This operator can be constructed in more than one way, and so we get more than one gauge theory. Two such gauge theories are the Stuckelberg theory, and the theory of Maxwell field interacting with an antisymmetric tensor field. We also show that the application of the projection operator does not affect the Lorentz invariance of this model.