Remarks on multisymplectic reduction

TL;DR

This paper discusses the reduction process of multisymplectic manifolds under Lie group actions, aiming to develop a covariant reduction scheme for classical field theories with symmetries.

Contribution

It introduces a framework for multisymplectic reduction, advancing the understanding of symmetry reduction in classical field theories.

Findings

Proposes a reduction scheme for multisymplectic manifolds.

Lays groundwork for covariant reduction in classical field theories.

Addresses the role of Lie group actions in multisymplectic geometry.

Abstract

The problem of reduction of multisymplectic manifolds by the action of Lie groups is stated and discussed, as a previous step to give a fully covariant scheme of reduction for classical field theories with symmetries.