Exact Solution of the Schwinger Model with Compact U(1)

TL;DR

This paper provides an exact solution to the Schwinger model with a compact U(1) gauge group, revealing unique spectral and charge properties due to topological constraints, differing from the standard model.

Contribution

It introduces a compact version of the Schwinger model with a topological gauge condition, leading to novel spectral and charge conservation features.

Findings

Zero mode spectrum is non-degenerate and not harmonic oscillator-like.

Electric and modified gauge-invariant chiral charges are conserved.

No $ heta$-vacuum is needed in this formulation.

Abstract

The exact solution of the Schwinger model with compact gauge group U(1) is presented. The compactification is imposed by demanding that the only surviving true electromagnetic degree of freedom has angular character. Not surprinsingly, this topological condition defines a version of the Schwinger model which is different from the standard one, where $c$ takes values on the line. The main consequences are: the spectra of the zero modes is not degenerated and does not correspond to the equally spaced harmonic oscillator, both the electric charge and a modified gauge invariant chiral charge are conserved (nevertheless, the axial-current anomaly is still present) and, finally, there is no need to introduce a $\theta$-vacuum. A comparison with the results of the standard Schwinger model is pointed out along the text.