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Keywords = presymplectic manifolds

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28 pages, 410 KiB  
Article
Symmetries and Covariant Poisson Brackets on Presymplectic Manifolds
by Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo, Luca Schiavone and Alessandro Zampini
Symmetry 2022, 14(1), 70; https://doi.org/10.3390/sym14010070 - 4 Jan 2022
Cited by 8 | Viewed by 2115
Abstract
As the space of solutions of the first-order Hamiltonian field theory has a presymplectic structure, we describe a class of conserved charges associated with the momentum map, determined by a symmetry group of transformations. A gauge theory is dealt with by using a [...] Read more.
As the space of solutions of the first-order Hamiltonian field theory has a presymplectic structure, we describe a class of conserved charges associated with the momentum map, determined by a symmetry group of transformations. A gauge theory is dealt with by using a symplectic regularization based on an application of Gotay’s coisotropic embedding theorem. An analysis of electrodynamics and of the Klein–Gordon theory illustrate the main results of the theory as well as the emergence of the energy–momentum tensor algebra of conserved currents. Full article
(This article belongs to the Special Issue Geometric Analysis of Nonlinear Partial Differential Equations II)
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