Gauge-invariant extensions of the Proca model in a noncommutative space-time

TL;DR

This paper explores how noncommutative space-time affects gauge invariance in the Proca model, constructing a gauge-invariant version using gauge unfixing and analyzing the impact of noncommutativity on symmetries.

Contribution

It introduces a gauge-invariant noncommutative Proca model using gauge unfixing and examines the influence of noncommutativity on gauge symmetries.

Findings

Successfully constructed a gauge-invariant NC Proca model

Demonstrated that NC parameters do not necessarily alter gauge symmetries

Provided a standard Poisson bracket analysis of the NC gauge symmetries

Abstract

The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac's classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories, are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.