Equations of Motion for Spinning Particles in External\\Electromagnetic and Gravitational Fields

TL;DR

This paper derives equations describing the motion and spin of a classical particle influenced by electromagnetic and gravitational fields, ensuring correct spin component constraints and analyzing deviations from geodesic and Fermi-Walker transport.

Contribution

It provides a derivation from an action principle that automatically satisfies spin constraints and describes particle dynamics beyond simple geodesic motion.

Findings

Spin is generally not Fermi-Walker transported.

Particle position does not follow a geodesic in general.

Deviations from geodesic and Fermi-Walker transport are typically small.

Abstract

The equations of motion for the position and spin of a classical particle coupled to an external electromagnetic and gravitational potential are derived from an action principle. The constraints insuring a correct number of independent spin components are automatically satisfied. In general the spin is not Fermi-Walker transported nor does the position follow a geodesic, although the deviations are small for most situations.