Extended test particles in geometric fields

Abstract

We treat the motion of an extended spinning test particle interacting with external fields belonging to a large class, which includes curvature, torsion, Maxwell, and Yang–Mills fields. We use a unified geometric description of all these fields based on a multidimensional space which generalizes the principal fiber bundle of the Lorentz frames. Guided by the work of Dixon, we give suitable definitions of the energy, the momentum, the angular momentum, the charge, and the isotopic spin of the extended particle, and we derive exact equations for the derivatives of these quantities. We discuss the pole–dipole approximation, and we compare our results with the special cases treated by other authors.