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arXiv · 2303.16037

Conditions for symmetry reduction of polysymplectic and polycosymplectic structures

Eduardo García-Toraño Andrés·Tom Mestdag
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Abstract

For Hamiltonian field theories on polysymplectic manifolds with a symmetry group action and a momentum map, we explore the redundancy in a set of necessary conditions that has appeared in the literature, for a generalized version of the Marsden-Weinstein symmetry reduction theorem. Next, we prove a necessary and sufficient condition for polycosymplectic reduction. We relate polycosymplectic reduction in a one-to-one way to the reduction of an associated larger polysymplectic manifold. Throughout the paper, we provide examples and discuss special cases.

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Eduardo García-Toraño Andrés, Tom Mestdag. 2023-03-28. Conditions for symmetry reduction of polysymplectic and polycosymplectic structures. https://doi.org/10.1088/1751-8121/ace74c

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