A general construction of Poisson brackets on exact multisymplectic manifolds

TL;DR

This paper introduces a new Poisson bracket for exact multisymplectic manifolds that applies to forms of any degree, addressing a long-standing problem in multisymplectic classical field theory.

Contribution

It provides a general construction of a Poisson bracket applicable to all form degrees in multisymplectic manifolds, with examples and key properties outlined.

Findings

The new bracket extends Poisson structures to arbitrary form degrees.

Examples demonstrate the bracket's applicability in multisymplectic geometry.

Properties of the bracket are established with proofs sketched.

Abstract

In this note the long standing problem of the definition of a Poisson bracket in the framework of a multisymplectic formulation of classical field theory is solved. The new bracket operation can be applied to forms of arbitary degree. Relevant examples are discussed and important properties are stated with proofs sketched.