Poisson-Poincaré reduction for Field Theories
arXiv:2210.14732 · doi:10.1016/j.geomphys.2023.104879
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-Poincaré reduction for field theories. This procedure is related to the Lagrange-Poincaré 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.
34 pages