Cotangent bundle reduction and Routh reduction for polysymplectic manifolds
Mathematical Physics
2022-10-06 v2 Differential Geometry
math.MP
Abstract
We discuss Lagrangian and Hamiltonian field theories that are invariant under a symmetry group. We apply the polysymplectic reduction theorem for both types of field equations and we investigate aspects of the corresponding reconstruction process. We identify the polysymplectic structures that lie at the basis of cotangent bundle reduction and Routh reduction in this setting and we relate them by means of the Routhian function and its associated Legendre transformation. We end the paper with examples that illustrate the applicability of our results.
Cite
@article{arxiv.2205.00309,
title = {Cotangent bundle reduction and Routh reduction for polysymplectic manifolds},
author = {Santiago Capriotti and Viviana Alejandra Díaz and Eduardo García-Toraño Andrés and Tom Mestdag},
journal= {arXiv preprint arXiv:2205.00309},
year = {2022}
}