The Poisson Bracket for Poisson Forms in Multisymplectic Field Theory

TL;DR

This paper introduces a new Poisson bracket for differential forms in multisymplectic field theory, establishing a Lie superalgebra structure on Poisson forms in the geometric formulation of classical field theories.

Contribution

It provides a general, well-defined Poisson bracket for differential forms on multisymplectic manifolds, extending the geometric framework of classical field theories.

Findings

Defines a Poisson bracket for Poisson forms in multisymplectic geometry

Establishes the Lie superalgebra structure of Poisson forms

Applies to exact multisymplectic manifolds in field theory

Abstract

We present a general definition of the Poisson bracket between differential forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories and, more generally, on exact multisymplectic manifolds. It is well defined for a certain class of differential forms that we propose to call Poisson forms and turns the space of Poisson forms into a Lie superalgebra.