Revisiting the dynamics of a charged spinning body in curved spacetime

We analyze the motion of the spinning body (in the pole-dipole approximation) in the gravitational and electromagnetic fields described by the Mathisson-Papapetrou-Dixon-Souriau equations. First, we define a novel spin supplementary condition for the electromagnetic interactions which generalizes the one proposed by Ohashi-Kyrian-Semer\'ak for gravity. As a result, we get the whole family of charged spinning particle models in the curved spacetime with remarkably simple dynamics (momentum and velocity are parallel). Applying the reparametrization procedure, for a specific dipole moment, we obtain equations of motion with constant mass and gyromagnetic factor. Next, we show that these equations follows from an effective Hamiltonian formalism, previously interpreted as a classical model of the charged Dirac particle.