The Renormalization of the Non-Abelian Gauge Theories in the Causal Approach

TL;DR

This paper investigates the gauge invariance and anomaly structure of non-Abelian gauge theories, specifically Yang-Mills, using the Epstein-Glaser causal approach to renormalization, confirming anomaly absence in QED.

Contribution

It applies the Epstein-Glaser causal approach to analyze gauge invariance and anomalies in non-Abelian gauge theories, providing a systematic framework for anomaly detection.

Findings

No anomalies in quantum electrodynamics at all orders

Generic form of anomalies in Yang-Mills models identified

Method confirms gauge invariance in QED through causal approach

Abstract

We consider the gauge invariance of the standard Yang-Mills model in the framework of the causal approach of Epstein-Glaser and Scharf and determine the generic form of the anomalies. The method used is based Epstein-Glaser approach to renormalization theory. In the case of quantum electrodynamics we obtain quite easily the absence of anomalies in all orders.