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Batalin-Vilkovisky formalism in the functional approach to classical field theory. (English) Zbl 1418.70034
Summary: 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.

MSC:
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
81T13 Yang-Mills and other gauge theories in quantum field theory
18A99 General theory of categories and functors
58E99 Variational problems in infinite-dimensional spaces
81T20 Quantum field theory on curved space or space-time backgrounds
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