Batalin–Vilkovisky Formalism as a Theory of Integration for Polyvectors

Abstract

The Batalin–Vilkovisky (BV) formalism is a powerful generalization of the BRST approach of gauge theories and allows to treat more general field theories. We will see how, starting from the case of a finite dimensional configuration space, we can see this formalism as a theory of integration for polyvectors over the shifted cotangent bundle of the configuration space and arrive at a formula that admits a generalization to the infinite dimensional case. The process of gauge fixing and the observables of the theory will be presented.