Electromagnetic dynamics and geometric transport in spin-nondegenerate SME particles

Abstract

We investigate the electromagnetic dynamics of spin-nondegenerate classical particle models arising from Lorentz-violating sectors of the Standard-Model Extension, focusing on the $b_\mu$ background. Starting from the type-2 relativistic Lagrangian, we introduce minimal electromagnetic coupling and derive the exact Hamiltonian dynamics associated with each sector in terms of the gauge-covariant kinetic momentum. The modified dispersion relation leads to a sector-dependent relation between velocity and momentum, which directly affects the response to external fields. In the presence of a uniform magnetic field, we show that the two sectors exhibit distinct cyclotron frequencies and radii, implying that even constant fields dynamically resolve the underlying structure of the theory. In the nonrelativistic regime, the Lorentz-violating background induces a sector-dependent modification of the transverse inertial response, which can be interpreted as an effective anisotropic mass. After projection onto a single sector, the reduced dynamics acquires a noncanonical symplectic structure. The equations of motion can be written in semiclassical form with an effective momentum space curvature $\Omega_{\pm}$, leading to anomalous velocity terms and a modified phase-space measure. As a consequence, a purely electric field generates opposite transverse drifts proportional to $q\,\mathbf{E} \times \Omega_{\pm}$, producing a Hall-like current without requiring a magnetic field.