  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.
