Symmetries and Covariant Poisson Brackets on Presymplectic Manifolds

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.

Automated summary

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 using Gotay's coisotropic embedding theorem. An analysis of electrodynamics and 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.