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

Klaus Fredenhagen, Katarzyna Rejzner

Published 2011-01-26, updated 2011-07-05Version 5

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.