Spinning Relativistic Particle in an External Electromagnetic Field

TL;DR

This paper develops a Hamiltonian framework for spinning relativistic particles in electromagnetic fields, revealing that particles with g=2 follow Lorentz force, while others experience an additional magnetic dipole force.

Contribution

It introduces a new Hamiltonian approach with specific coordinates and constraints to describe spin dynamics in external fields.

Findings

Particles with g=2 follow standard Lorentz force.

Particles with g≠2 experience an additional magnetic dipole force.

The formulation provides a consistent way to include spin in relativistic particle dynamics.

Abstract

The Hamiltonian formulation of the motion of a spinning relativistic particle in an external electromagnetic field is considered. The approach is based on the introduction of new coordinates and their conjugated momenta to describe the spin degrees of freedom together with an appropriate set of constraints in the Dirac formulation. For particles with gyromagnetic ratio $g=2$, the equations of motion do not predict any deviation from the standard Lorentz force, while for $g \neq 2$ an additional force, which corresponds to the magnetic dipole force, is obtained.