Ward identities and renormalization of general gauge theories

Abstract

We introduce the concept of general gauge theory which includes Yang–Mills models. We use 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. For the Yang–Mills model we provide these identities in the lowest orders of the perturbation theory and prove that they are valid. The investigation of higher orders of the perturbation theory is still an open problem.