A Generalized Gauge Invariant Regularization of the Schwinger Model

TL;DR

This paper introduces a new one-parameter family of gauge invariant regularizations for the Schwinger model, revealing that the spectrum remains largely unchanged except at a specific parameter value where free fermions emerge.

Contribution

It proposes a generalized regularization scheme that preserves gauge invariance and extends previous methods like point-splitting and Fujikawa's approach.

Findings

Spectrum remains qualitatively unchanged under the new regularization.

A limiting parameter value leads to the appearance of free fermions.

The regularization preserves gauge invariance across the parameter range.

Abstract

The Schwinger model is studied with a new one - parameter class of gauge invariant regularizations that generalizes the usual point - splitting or Fujikawa schemes. The spectrum is found to be qualitatively unchanged, except for a limiting value of the regularizing parameter, where free fermions appear in the spectrum.