Lectures on BRS invariance for massive boson fields

Abstract

These notes correspond to lectures given at the Villa de Leyva Summer School in Colombia (July 2007). Our main purpose in this short course on BRS invariance of gauge theories is to illuminate corners of the theory left in the shade by standard treatments. The plan is as follows. First a review of Utiyama's "general gauge theory". Promptly we find a counterexample to it in the shape of the massive spin-1 Stueckelberg gauge field. This is not fancy, as the massive case is the most natural one to introduce BRS invariance in the context of free quantum fields. Mathematically speaking, the first part of the course uses Utiyama's notation, and thus has the flavour and non-intrinsic notation of standard physics textbooks. Next we deal with boson fields on Fock space and BRS invariance in connection with the existence of Krein operators; the attending rigour points are then addressed.