Gauge-Free Hamiltonian Structure of the Spin Maxwell-Vlasov Equations

We derive the gauge-free Hamiltonian structure of an extended kinetic theory, for which the intrinsic spin of the particles is taken into account. Such a semi-classical theory can be of interest for describing, e.g., strongly magnetized plasma systems. We find that it is possible to construct generalized brackets for the extended phase space, and discuss the implications of our findings.