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.

References in corpus (9)

• Geometric formulation of the Covariant Phase Space methods with boundaries
• Covariant canonical formulations of classical field theories
• Covariant Jacobi Brackets for Test Particles
• Covariant Variational Evolution and Jacobi Brackets: Fields
• A review on geometric formulations for classical field theory: the Bonzom-Livine model for gravity
• Symmetries and gauge symmetries in multisymplectic first and second-order Lagrangian field theories: electromagnetic and gravitational fields
• Covariant Brackets for Particles and Fields
• Evolutionary equations and constraints: Maxwell equations
• Symmetries and Reduction. Part II - Lagrangian and Hamilton-Jacobi picture

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