$n$-plectic Maxwell Theory

TL;DR

This paper explores the multisymplectic formulation of Maxwell's theory, focusing on DeDonder-Weyl theory, observable forms, and the construction of higher Lepage-Dedecker correspondence in two dimensions.

Contribution

It provides a detailed multisymplectic treatment of Maxwell theory, including algebraic and dynamical observable forms and insights into higher Lepage-Dedecker correspondence.

Findings

Analysis of DeDonder-Weyl theory in Maxwell context

Identification of algebraic and dynamical observable forms

Initial steps towards higher Lepage-Dedecker correspondence in 2D

Abstract

This note provides a detailed treatment of the Multisymplectic Maxwell theory through the general setting developed in [24] [26] [27]. In particular we explore the DeDonder-Weyl theory, the question of algebraic and dynamical observable forms, the copolarization process related to the good search of canonical forms. Finally, we give - for the two dimensional case - some indications for the construction of the higher Lepage-Dedecker correspondence, in the context of the underlying Grassmannian viewpoint.