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Batalin-Vilkovisky Formalism in the Functional Approach to Classical Field Theory

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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.

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  1. II Inst. f. Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761, Hamburg, Germany

    Klaus Fredenhagen & Katarzyna Rejzner

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  1. Klaus Fredenhagen
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  2. Katarzyna Rejzner
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Correspondence to Klaus Fredenhagen.

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Communicated by M. Salmhofer

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Fredenhagen, K., Rejzner, K. Batalin-Vilkovisky Formalism in the Functional Approach to Classical Field Theory. Commun. Math. Phys. 314, 93–127 (2012). https://doi.org/10.1007/s00220-012-1487-y

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