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

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.

42 pages, improved formulation, typos corrected