A general theory for gauge-free lifting

TL;DR

This paper develops a comprehensive gauge-free framework for lifting particle equations of motion to coupled Hamiltonian Vlasov-Maxwell systems, generalizing plasma physics models with explicit polarization and magnetization expressions.

Contribution

It introduces a general gauge-free lifting theory for charged particle dynamics to Hamiltonian Vlasov-Maxwell equations, including new models with spin and magnetic monopoles.

Findings

Provides explicit polarization and magnetization expressions in terms of particle dynamics.

Shows all models are Hamiltonian and satisfy the Jacobi identity.

Includes examples with spin and magnetic monopoles.

Abstract

A theory for lifting equations of motion for charged particle dynamics, subject to given electromagnetic like forces, up to a gauge-free system of coupled Hamiltonian Vlasov-Maxwell like equations is given. The theory provides very general expressions for the polarization and magnetization vector fields in terms of the particle dynamics description of matter. Thus, as is common in plasma physics, the particle dynamics replaces conventional constitutive relations for matter. Several examples are considered including the usual Vlasov-Maxwell theory, a guiding center kinetic theory, Vlasov-Maxwell theory with the inclusion of spin, and a Vlasov-Maxwell theory with the inclusion of Dirac's magnetic monopoles. All are shown to be Hamiltonian field theories and the Jacobi identity is proven directly.