Hamiltonian Vector Fields on Multiphase Spaces of Classical Field Theory

TL;DR

This paper classifies Hamiltonian vector fields on multisymplectic and polysymplectic fiber bundles, providing a framework similar to that used for dual jet bundles in classical field theories.

Contribution

It offers a new classification of Hamiltonian vector fields on multiphase spaces, extending known results to these geometric structures in classical field theory.

Findings

Classification of Hamiltonian vector fields on multiphase spaces

Analogous results to dual jet bundle classifications

Framework applicable to multisymplectic and polysymplectic approaches

Abstract

We present a classification of hamiltonian vector fields on multisymplectic and polysymplectic fiber bundles closely analogous to the one known for the corresponding dual jet bundles that appear in the multisymplectic and polysymplectic approach to first order classical field theories.