Batalin-Vilkovisky formalism as a theory of integration for polyvectors

TL;DR

This paper interprets the Batalin-Vilkovisky formalism as a comprehensive integration theory for polyvector fields on shifted cotangent bundles, extending from finite to infinite-dimensional cases.

Contribution

It provides a geometric interpretation of the BV formalism as an integration theory for polyvectors, generalizing to infinite-dimensional field theories.

Findings

Formulation of BV as a polyvector integration theory

Extension from finite to infinite-dimensional cases

Inclusion of gauge fixing and observables in the formalism

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.