Batalin-Vilkovisky formalism in the functional approach to classical field theory

TL;DR

This paper extends the Batalin-Vilkovisky formalism to classical field theories on general spacetimes, emphasizing local covariance and homological methods to construct the algebra of observables, including in gravity.

Contribution

It introduces a local covariant BV formalism for classical fields, enabling a homological construction of observables in gravity without fixed spacetime backgrounds.

Findings

Developed BV formalism on globally hyperbolic spacetimes

Achieved a homological construction of the Poisson algebra in gravity

Emphasized the importance of local covariance in the formalism

Abstract

We develop the Batalin-Vilkovisky formalism for classical field theory on generic globally hyperbolic spacetimes. A crucial aspect of our treatment is the incorporation of the principle of local covariance which amounts to formulate the theory without reference to a distinguished spacetime. In particular, this allows a homological construction of the Poisson algebra of observables in classical gravity. Our methods heavily rely on the differential geometry of configuration spaces of classical fields.