A Poisson Bracket on Multisymplectic Phase Space

TL;DR

This paper introduces a novel Poisson bracket for Hamiltonian forms in multisymplectic phase space, satisfying Jacobi's identity for certain forms, advancing the mathematical framework of multisymplectic geometry.

Contribution

The paper defines a new Poisson bracket on multisymplectic phase space that adheres to Jacobi's identity for forms of degree n-1, enhancing the theoretical structure.

Findings

Poisson bracket defined for Hamiltonian forms

Jacobi's identity holds for forms of degree n-1

Advances multisymplectic geometric framework

Abstract

A new Poisson bracket for Hamiltonian forms on the full multisymplectic phase space is defined. At least for forms of degree n-1, where n is the dimension of space-time, Jacobi's identity is fulfilled.