The polysymplectic Hamiltonian formalism in field theory and calculus of variations I: The local case

Abstract

An invariant geometric Hamiltonian formalism for multiple integral variational problems and field theories is presented. The formalism is based on the notion of a polysymplectic form, which is a vector valued generalization of symplectic forms. Hamiltonian equations, canonical transformations, Lagrange systems, symmetries, field theoretic momentum mappings and a classification of G-homogeneous field theoretic systems on a generalization of coadjoint orbits are investigated. © 1987, International Press of Boston, Inc. All Rights Reserved.