The Relativistic Stern-Gerlach Force

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].

In this revised version of the paper, the Stern-Gerlach component of the canonical momentum is treated as velocity-independent in analogy to the electromagnetic momentum, and its time derivative is simplified by inserting the known time derivative of the spin