Consistent anomaly

Abstract

AbstractChapter 4 introduced the anomaly as the breakdown of a classical conservation law. This chapter investigates the anomaly further in light of gauge transformations. Section 8.1 introduces an infinitestimal gauge operator, generalize to a BRS operator, and find its representation in the functional space of the gauge potentials and Faddeev–Popov ghosts. Section 8.2 discusses the anomalous Ward identity in terms of functional derivatives and subsequently derives the equation which determines the anomaly — the Wess–Zumino consistency condition — in the gauge transformation variant and in the BRS variant. Section 8.3 presents the different aspects of the anomaly equation, such as the algebra-, the cocycle-, and the cohomology aspects.