Equations of Motion of Spinning Relativistic Particles

TL;DR

This paper investigates the motion of spinning relativistic particles in external fields, identifies issues with covariant equations, and proposes a self-consistent, noncovariant approach that includes higher-order spin effects and the gravimagnetic moment.

Contribution

It introduces a self-consistent noncovariant framework for describing spinning relativistic particles, addressing covariant equation pathologies and extending to higher-order spin effects.

Findings

Covariant equations exhibit pathological solutions when treated nonperturbatively in spin.

A simple first-order gravitational interaction description is provided.

Explicit second-order Hamiltonian expression is derived.

Abstract

The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. Covariant equations for this motion are demonstrated to possess pathological solutions, when treated nonperturbatively in spin. A self-consistent approach to the problem is formulated, based on the noncovariant description of spin and on the usual, ``naive'' definition of the coordinate of a relativistic particle. A simple description of the gravitational interaction of first order in spin, is pointed out for a relativistic particle. The approach developed allows one to consider effects of higher order in spin. Explicit expression for the second-order Hamiltonian is presented. We discuss the gravimagnetic moment, which is a special spin effect in general relativity.