On the Renormalizability of Theories with Gauge Anomalies

TL;DR

This paper investigates the renormalization process of two (1+1)-dimensional gauge theories with gauge anomalies, demonstrating the necessity of using the complete photon propagator for consistent loop calculations.

Contribution

It introduces a semi-perturbative renormalization method for anomalous gauge theories, addressing divergences in fermionic Green's functions without gauge invariance.

Findings

Photon propagator is ill-defined at tree level in these models

Complete photon propagator must be used in loop calculations

Renormalization is successfully performed to one loop level

Abstract

We consider the detailed renormalization of two (1+1)-dimensional gauge theories which are quantized without preserving gauge invariance: the chiral and the "anomalous" Schwinger models. By regularizing the non-perturbative divergences that appear in fermionic Green's functions of both models, we show that the "tree level" photon propagator is ill-defined, thus forcing one to use the complete photon propagator in the loop expansion of these functions. We perform the renormalization of these divergences in both models to one loop level, defining it in a consistent and semi-perturbative sense that we propose in this paper.