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

Understand

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.