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

TL;DR

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

Contribution

It presents the first complete Hamiltonian solution of the compact U(1) Schwinger model, highlighting its distinct spectral, charge, and topological 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 complete exact solution of the Schwinger model with compact gauge group U(1), in the Hamiltonian approach, 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.