On gauge invariance of Yang-Mills theories with matter fields

Abstract

We continue the investigation of quantied Yang-Mills theories coupled to matter fields in the framework of causal perturbation theory. In this approach, which goes back to Epstein and Glaser, one works with free fields throughout, so that all expressions are mathematically well defined. The general proof of theCg-identities (C-number identities expressing gauge invariance) is completed. We attach importance to the correct treatment of the degenerate terms and to theCg-identities with external matter legs. Moreover, the compatibility of allCg-identities withP-, T-, C-invariance and pseudo-unitarity is shown.