A general theory for gauge-free lifting

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.

References in corpus (3)

• Quantum plasma effects in the classical regime
• Effects of the $g$-factor in semi-classical kinetic plasma theory
• Hamiltonian magnetohydrodynamics: symmetric formulation, Casimir invariants, and equilibrium variational principles

Cited by in corpus (9)

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• Variational approach to low-frequency kinetic-MHD in the current coupling scheme
• The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems
• Hamiltonian and action formalisms for two-dimensional gyroviscous MHD
• Gauge-free electromagnetic gyrokinetic theory
• On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets
• Higher order Hamiltonian fluid reduction of Vlasov equation
• The action principle for generalized fluid motion including gyroviscosity
• Hamiltonian structure of the guiding-center Vlasov-Maxwell equations