Gauge Invariant Formulation and Bosonisation of the Schwinger Model

TL;DR

This paper presents a gauge-invariant formulation of the massless Schwinger model in 1+1 dimensions, providing a natural bosonisation scheme and insights into the bosonisation process, including a calculation of the chiral anomaly.

Contribution

It introduces a gauge-invariant approach to the Schwinger model that naturally leads to bosonisation and offers deeper understanding of the bosonisation phenomenon.

Findings

Derivation of the bosonisation rule from gauge-invariant variables

Calculation of the chiral anomaly within the new formulation

Deeper insight into the nature of bosonisation in 1+1 dimensions

Abstract

The functional integral of the massless Schwinger model in $(1+1)$ dimensions is reduced to an integral in terms of local gauge invariant quantities. It turns out that this approach leads to a natural bosonisation scheme, yielding, in particular the famous `bosonisation rule'' and giving some deeper insight into the nature of the bosonisation phenomenon. As an application, the chiral anomaly is calculated within this formulation.