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The Bargmann-Michel-Telegdi equations describing the motions of a spinning,charged, relativistic particle endowed with an anomalous magnetic moment in anelectromagnetic field, are reconsidered. They are shown to duly stem from thelinearization of the characteristic distribution of a pre-symplectic structurerefining the original one of Souriau. In this model, once specialized to thecase of a static electric-like field, the angular momentum and energy given bythe 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.

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