The Schwinger and Chiral Schwinger Models in a Non-perturbative Spectral Regularization

TL;DR

This paper demonstrates that spectral regularization provides a consistent, divergence-free method for analyzing gauge symmetry and anomalies in the Schwinger and chiral Schwinger models in 1+1 dimensions, avoiding ambiguities.

Contribution

It introduces spectral regularization as a non-perturbative, ambiguity-free scheme that accurately captures gauge invariance and anomalies in these models.

Findings

Spectral regularization yields consistent two-point functions.

It correctly displays gauge invariance in the Schwinger model.

It reproduces the axial anomaly in the chiral Schwinger model.

Abstract

We investigate the employment of a non-perturbative regularization scheme -- the spectral regularization, which is based on the gauge technique, previously implemented in the context of chiral quark models -- in the study of the gauge symmetry preservation within the Schwinger model and violation in the chiral Schwinger model. We show that the spectral regularization provides mathematical consistent and ambiguity free solutions for the two-point functions of both Schwinger and chiral Schwinger models in exact (1+1) dimensions, correctly displaying the gauge invariance in the Schwinger model and the axial anomaly in the chiral Schwinger model. The employment of the spectral regularization avoids any dependence on ambiguous amplitudes and/or unconventional $\gamma^5$ algebra. Our results reinforce the strength of the spectral regularization as a mathematical consistent, divergence free, and ambiguity free regularization scheme that correctly implements symmetry conservation or violation in each case.