Yang-Mills Gauge Theories

Abstract

In this chapter we shall deal with Ward identities and with their renormalization in the case of a local invariance. We shall restrict the discussion here to Yang-Mills theories in four-dimensional space-time. Beyond their obvious physical relevance [2], these theories have played an eminent historical role. It was indeed in the search for a rigorous renormalization scheme for these theories that Becchi, Rouet and Stora [15, 16] in 1974 discovered BRS invariance and demonstrated its role in guarantying the unitarity of the S-matrix and the gauge independence of the physical observables, on the one hand, and set up the general iterative construction needed in the absence of an invariant regularization. Precisely the latter approach is called “algebraic renormalization” in the present book.