Poisson-Poincar\'e reduction for Field Theories
Differential Geometry
2023-06-28 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2210.14732,
title = {Poisson-Poincar\'e reduction for Field Theories},
author = {Miguel Á. Berbel and Marco Castrillón López},
journal= {arXiv preprint arXiv:2210.14732},
year = {2023}
}
Comments
34 pages