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arXiv · 2210.14732

Poisson-Poincar\'e reduction for Field Theories

Miguel Á. Berbel·Marco Castrillón López
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Abstract

Given a Hamiltonian system on a fiber bundle, there is a Poisson covariant formulation of the Hamilton equations. When a Lie group G acts freely, properly, preserving the fibers of the bundle and the Hamiltonian density is G-invariant, we study the reduction of this formulation to obtain an analogue of Poisson-Poincar\'e reduction for field theories. This procedure is related to the Lagrange-Poincar\'e reduction for field theories via a Legendre transformation. Finally, an application to a model of a charged strand evolving in an electric field is given.

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BibTeXRIS

Miguel Á. Berbel, Marco Castrillón López. 2022-10-26. Poisson-Poincar\'e reduction for Field Theories. https://doi.org/10.1016/j.geomphys.2023.104879

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