Maxwell's equations in media as a contact Hamiltonian vector field and its information geometry -- An approach with a bundle whose fiber is a contact manifold

TL;DR

This paper reformulates Maxwell's equations in media using contact Hamiltonian vector fields within a fiber bundle framework, linking electromagnetic energy, duality, and information geometry for a novel geometric perspective.

Contribution

It introduces a geometric formulation of Maxwell's equations as contact Hamiltonian systems on a fiber bundle, incorporating Legendre duality and information geometry.

Findings

Maxwell's equations are expressed as contact Hamiltonian vector fields.

Legendre duality relates energy and co-energy formulations.

Information geometry of Maxwell fields is established.

Abstract

It is shown that Maxwell's equations in media without source can be written as a contact Hamiltonian vector field restricted to a Legendre submanifold, where this submanifold is in a fiber space of a bundle and is generated by either electromagnetic energy functional or co-energy functional. Then, it turns out that Legendre duality for this system gives the induction oriented formulation of Maxwell's equations and field intensity oriented one. Also, information geometry of the Maxwell fields is introduced and discussed.