Stability and renormalization of Yang-Mills theory with Background Field Method: a regularization independent proof

TL;DR

This paper proves the stability and renormalizability of Yang-Mills theory in the Background Field Gauge using Ward and Slavnov-Taylor identities, providing a regularization independent framework.

Contribution

It offers a novel, regularization independent proof of Yang-Mills theory's stability and renormalizability in the Background Field Gauge, including a method for constructing counterterms.

Findings

Stability of the classical Yang-Mills model established

Renormalizability verified without regularization dependence

Counterterm construction method provided

Abstract

In this paper the stability and the renormalizability of Yang-Mills theory in the Background Field Gauge are studied. By means of Ward Identities of Background gauge invariance and Slavnov-Taylor Identities the stability of the classical model is proved and, in a regularization independent way, its renormalizability is verified. A prescription on how to build the counterterms is given and the possible anomalies which may appear for Ward Identities and for Slavnov-Taylor Identities are shown.