Symmetries and Covariant Poisson brackets on pre-symplectic manifolds

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.

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Cited by in corpus (5)

• Covariant canonical formulations of classical field theories
• Reductions: precontact versus presymplectic
• Basic notions of Poisson and symplectic geometry in local coordinates, with applications to Hamiltonian systems
• Poisson-Poincaré reduction for Field Theories
• The Geometry of the solution space of first order Hamiltonian field theories I: from particle dynamics to free Electrodynamics