Revisiting the dynamics of a charged spinning body in curved spacetime

TL;DR

This paper introduces a new spin condition for charged spinning bodies in curved spacetime, simplifying their dynamics and linking them to a classical model of the charged Dirac particle through an effective Hamiltonian.

Contribution

It proposes a novel spin condition that generalizes previous models, leading to simplified equations of motion and a Hamiltonian formalism for charged spinning bodies in curved spacetime.

Findings

Derived a family of models with simple dynamics where momentum and velocity are parallel.

Obtained equations of motion with constant mass and gyromagnetic ratio.

Connected the classical model to the charged Dirac particle via Hamiltonian formalism.

Abstract

We analyse 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 condition for the body with the magnetic dipole moment proportional to spin, 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 follow from an effective Hamiltonian formalism, previously interpreted as a classical model of the charged Dirac particle.