On the Bargmann-Michel-Telegdi equations, and spin-orbit coupling: a tribute to Raymond Stora

TL;DR

This paper revisits the Bargmann-Michel-Telegdi equations for spinning charged particles, showing they derive from a refined pre-symplectic structure, and correctly incorporate spin-orbit coupling in specific electromagnetic fields.

Contribution

It demonstrates that the BMT equations originate from a linearized pre-symplectic structure, refining previous models and accurately capturing spin-orbit coupling effects.

Findings

BMT equations derived from a refined pre-symplectic structure

Correct inclusion of spin-orbit coupling in static electric fields

Advancement in geometric understanding of spinning particle dynamics

Abstract

The Bargmann-Michel-Telegdi equations describing the motions of a spinning, charged, relativistic particle endowed with an anomalous magnetic moment in an electromagnetic field, are reconsidered. They are shown to duly stem from the linearization of the characteristic distribution of a pre-symplectic structure refining the original one of Souriau. In this model, once specialized to the case of a static electric-like field, the angular momentum and energy given by the associated moment map now correctly restore the spin-orbit coupling term. This is the state-of-the-art of unfinished joint work with Raymond Stora.