Renormalization Proof for Spontaneously Broken Yang–Mills Theory with Flow Equations

Abstract:

In this paper we present a renormalizability proof for spontaneously broken SU(2) gauge theory. It is based on Flow Equations, i.e. on the Wilson renormalization group adapted to perturbation theory. The power counting part of the proof, which is conceptually and technically simple, follows the same lines as that for any other renormalizable theory. The main difficulty stems from the fact that the regularization violates gauge invariance. We prove that there exists a class of renormalization conditions such that the renormalized Green functions satisfy the Slavnov–Taylor identities of SU(2) Yang–Mills theory on which the gauge invariance of the renormalized theory is based.