Hamiltonian coupling of electromagnetic field and matter

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 of transport of mixtures with electrodynamics is elucidated.