Symmetries and Covariant Poisson brackets on pre-symplectic manifolds
Mathematical Physics
2022-06-23 v1 Differential Geometry
math.MP
Abstract
Noticing that the space of the solutions of a first order Hamiltonian field theory has a pre-symplectic structure, we describe a class of conserved charges on it associated to the momentum map determined by any symmetry group of transformations. Gauge theories are dealt with by using a symplectic regularization based on an application of Gotay's coisotropic embedding theorem. The analysis of Electrodynamics and of the Klein-Gordon theory illustrates the main results of the theory as well as the emergence of the energy-momentum tensor algebra of conserved currents.
Keywords
Cite
@article{arxiv.2111.13066,
title = {Symmetries and Covariant Poisson brackets on pre-symplectic manifolds},
author = {Florio M. Ciaglia and Fabio Di Cosmo and Alberto Ibort and Giuseppe Marmo and Luca Schiavone and Alessandro Zampini},
journal= {arXiv preprint arXiv:2111.13066},
year = {2022}
}