The Relativistic Stern-Gerlach Force

TL;DR

This paper derives the relativistic Stern-Gerlach and Thomas precession forces for spinning particles in electromagnetic fields, correcting previous misconceptions about the force's gamma-squared dependence.

Contribution

It provides a new derivation of the relativistic forces from the Lagrangian, clarifying the force's dependence on gamma and correcting prior claims.

Findings

The longitudinal component of the force lacks a gamma-squared term.

The derivation is based on the Lagrangian in the laboratory frame.

The results correct previous misconceptions about the force's gamma dependence.

Abstract

The relativistic Lagrangian for a spinning particle in an electromagnetic field is derived from the known Lagrangian in the particle's rest frame. The resulting relativistic Stern-Gerlach and Thomas precession forces on the particle are then derived from the Lagrangian in the laboratory frame. In particular, the longitudinal component of this combined Stern-Gerlach-Thomas force does not contain a term proportional to gamma-squared as was claimed in a previous derivation [1].