Renormalization and Gauge Independence in Spontaneously Broken Gauge Theories

Abstract

We discuss the renormalization of spontaneously broken gauge theories in a large class of renormalizable gauges which includes the unitary gauge as a singular limit. Particular attention is paid to the constraints of gauge invariance on the renormalization program and to the gauge invariance and finiteness of the $S$ matrix. Our intention is to supplement the formal discussions already in the literature by carrying out the renormalization program in an explicit and complete way (fixing counterterms and defining the physical parameters), and by restricting demonstrations of gauge invariance and finiteness to the one-loop level. The discussion is limited to an Abelian model for simplicity, and can easily be extended to more complicated gauge theories. All the essential features, however, are found already in the Abelian model.