Slavnov-Taylor Identities from the Causal Point of View

TL;DR

This paper proves that Slavnov-Taylor identities, crucial for gauge invariance in Yang-Mills theories, hold within the causal perturbation theory framework, connecting two definitions of Green's functions.

Contribution

It demonstrates the validity of Slavnov-Taylor identities in the Epstein-Glaser causal approach to quantized gauge theories.

Findings

Slavnov-Taylor identities are derived from simple gauge transformations.

The paper shows the equivalence of Epstein-Glaser and Gell-Mann Low Green's functions.

Gauge invariance is maintained in the causal perturbation framework.

Abstract

We continue the investigation of quantized Yang-Mills theories coupled to matter fields in the framework of causal perturbation theory which goes back to Epstein and Glaser. In this approach gauge invariance is expressed by a simple commutator relation for the S-matrix and the corresponding gauge transformations are simple transformations of the free fields only. In spite of this simplicity, gauge invariance implies the usual Slavnov-Taylor identities. The main purpose of this paper is to prove the latter statement. Since the Slavnov-Taylor identities are formulated in terms of Green's functions, we investigate the agreement of two perturbative definitions of Green's functions, namely of Epstein and Glaser's definition with the Gell-Mann Low series.