Hamiltonian reduction in affine principal bundles

Abstract

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This paper presents a Hamiltonian reduction procedure for field theo-ries over affine principal bundles introducing a canonical identification todescribe the reduced multisymplectic space without the introduction of aconnection. The main goal is to provide a Hamiltonian analogue of the La-grangian reduction theory developed in [4]. The core of this work lies in thederivation of this canonical identification, the reduced Hamilton–Cartanequations, and a reduced covariant bracket that describes the dynamics. Fi-nally, this theoretical framework is illustrated with a fundamental example:molecular strands