Poisson-Poincare reduction for field theories

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-Poincare reduction for field theories. This procedure is related to the Lagrange-Poincare 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. & COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by-nc -nd /4 .0/).

Automated summary

A Poisson covariant formulation of the Hamilton equations is studied for a Hamiltonian system on a fiber bundle. When a Lie group G acts freely, properly, preserving the fibers of the bundle and the Hamiltonian density is G-invariant, the reduction of this formulation is examined to obtain an analogue of Poisson-Poincare reduction for field theories. This procedure is related to the Lagrange-Poincare reduction for field theories through a Legendre transformation. Finally, an application to a model of a charged strand evolving in an electric field is given.