Slavnov-Taylor Identities from the Causal Point of View

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.

arXiv comment29 pages. The paper is written in TEX. The necessary macros are included. The figures are not done by computer, they can be ordered at the authors address

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