Hamiltonian Multivector Fields and Poisson Forms in Multisymplectic Field Theory

TL;DR

This paper classifies Hamiltonian multivector fields and Poisson forms in multisymplectic field theory, laying groundwork for explicit Poisson bracket calculations in geometric classical field theory.

Contribution

It provides a comprehensive classification of Hamiltonian multivector fields and Poisson forms in the multisymplectic framework, essential for computing Poisson brackets.

Findings

Classification of Hamiltonian multivector fields established

Classification of Poisson forms completed

Facilitates explicit Poisson bracket computations

Abstract

We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing explicit expressions for the Poisson bracket between two Poisson forms.