The Relation Between Gauge and Non-Gauge Abelian Models

TL;DR

This paper explores the connection between gauge-invariant and non gauge-invariant Abelian vector models, demonstrating that models like Proca and Chiral Schwinger can be viewed as gauge-fixed versions of gauge-invariant theories, establishing a fundamental equivalence.

Contribution

It introduces a method to interpret non gauge-invariant Abelian models as gauge-fixed forms of gauge-invariant models, unifying their understanding.

Findings

Proca and Chiral Schwinger models are gauge-fixed versions of gauge-invariant models.

A gauge-invariant form of the chiral Schwinger model corresponds to the two-dimensional Stueckelberg model.

Any consistent Abelian vector model without gauge symmetry can be seen as a gauge-fixed gauge theory.

Abstract

This work studies the relationship between gauge-invariant and non gauge-invariant abelian vector models. Following a technique introduced by Harada and Tsutsui, we show that the Proca and the Chiral Schwinger models may both be viewed as gauge-fixed versions of genuinely gauge- invariant models. This leads to the proposal that any consistent Abelian vector model with no gauge symmetry can be understood as a gauge theory that had its gauge fixed, which establishes an equivalence between gauge-invariant and non gauge-invariant models. Finally, we show that a gauge-invariant version of the chiral Schwinger model, after integrating out the fermionic degrees of freedom, can be identified with the two-dimensional Stueckelberg model without the gauge fixing term.