Removal of divergences with the Batalin-Vilkovisky formalism

Abstract

We show how to remove the divergences in an arbitrary gauge-field theory (possibly nonrenormalizable, i.e. involving infinitely many parameters) in the contex of the Batalin-Vilkovisky formalism. We show that this can be achieved by performing, order by order in the loop expansion, a redefinition of the parameters of the classical Lagrangian (possibly infinitely many) and a canonical transformation (in the sense of Batalin and Vilkovisky) of fields and BRS sources. Gauge-invariance is turned into a suitable quantum generalization of BRS invariance. We define quantum observables in this formal context and study their properties. We show the independence of the on-shell physical amplitudes from gauge fixing. We apply the result to renormalizable gauge-field theories that are gauge-fixed with a non-renormalizable gauge fixing and prove that their predictivity is retained. A corollary is that topological field theories are predictive.