Hamiltonian Coupling of Electromagnetic Field and Matter

TL;DR

This paper explores geometric methods for constructing and coupling Poisson brackets to model the Hamiltonian dynamics of electromagnetic fields interacting with matter, clarifying their mathematical structure.

Contribution

It introduces geometric techniques for constructing coupled Poisson brackets and applies them to Hamiltonian modeling of electromagnetic-matter interactions.

Findings

Elucidation of Hamiltonian coupling mechanisms

Development of geometric Poisson bracket construction methods

Application to electromagnetic and matter transport systems

Abstract

Reversible part of evolution equations of physical systems is often generated by a Poisson bracket. We discuss geometric means of construction of Poisson brackets and their mutual coupling (direct, semidirect and matched-pair products) as well as projections of Poisson brackets to less detailed Poisson brackets. This way the Hamiltonian coupling between transport of mixtures and electrodynamics is elucidated.