Brackets in multicontact geometry and multisymplectization

TL;DR

This paper introduces a graded bracket for forms on multicontact manifolds, extending contact geometry, and develops multisymplectization to connect with multisymplectic geometry, with applications to dissipative field theories.

Contribution

It defines a new graded bracket satisfying Jacobi and Leibniz identities on multicontact manifolds and develops multisymplectization linking these structures to multisymplectic geometry.

Findings

Defined a graded bracket satisfying Jacobi identity.

Developed multisymplectization for multicontact structures.

Applied framework to classical dissipative field theories.

Abstract

In this paper we introduce a graded bracket of forms on multicontact manifolds. This bracket satisfies a graded Jacobi identity as well as two different versions of the Leibniz rule, one of them being a weak Leibniz rule, extending the well-known notions in contact geometry. In addition, we develop the multisymplectization of multicontact structures to relate these brackets to the ones present in multisymplectic geometry and obtain the field equations in an abstract context. The Jacobi bracket also permits to study the evolution of observables and study the dissipation phenomena, which we also address. Finally, we apply the results to classical dissipative field theories.