Ward Identities and Renormalization of General Gauge Theories

TL;DR

This paper develops a framework for analyzing gauge theories, demonstrating that anomalies are confined to the vacuum sector and establishing the renormalizability of Yang-Mills models across all perturbation orders.

Contribution

It introduces a general gauge theory framework and proves the absence of anomalies in higher orders, simplifying renormalizability proofs for Yang-Mills models.

Findings

Anomalies occur only in the vacuum sector.

Renormalizability of Yang-Mills models is confirmed in all orders.

Simplifies the proof of renormalizability by reducing it to lower-order calculations.

Abstract

We introduce the concept of general gauge theory which includes Yang-Mills models. In the framework of the causal approach and show that the anomalies can appear only in the vacuum sector of the identities obtained from the gauge invariance condition by applying derivatives with respect to the basic fields. Then we provide a general result about the absence of anomalies in higher orders of perturbation theory. This result reduces the renormalizability proof to the study of lower orders of perturbation theory. For the Yang-Mills model one can perform this computation explicitly and obtains its renormalizability in all orders.