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 presymplectic 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.
Highlights
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
I have been informed by Serge Lazzarini that Raymond Stora and Valentine Telegdi were discussing, at CERN, an issue related to the expression of the spin-orbit coupling term in Souriau’s classical presymplectic model of spinning particles leading to the Bargmann-Michel-Telegdi (BMT) equations
A number of stimulating exchanges with him convinced me that the Souriau model should be somehow revisited so as to yield again the “robust” BMT equations as well as the correct expression of the spin-orbit term, effectively model-dependent in the considered classical framework, and which was missing in the abovementioned model
Summary
I have been informed by Serge Lazzarini that Raymond Stora and Valentine Telegdi were discussing, at CERN, an issue related to the expression of the spin-orbit coupling term in Souriau’s classical presymplectic model of spinning particles leading to the Bargmann-Michel-Telegdi (BMT) equations. A number of stimulating exchanges with him convinced me that the Souriau model (recalled in Section 3) should be somehow revisited so as to yield again the “robust” BMT equations as well as the correct expression of the spin-orbit term, effectively model-dependent in the considered classical framework, and which was missing in the abovementioned model In his carefully hand-written notes, Stora put forward an ingenious Ansatz, presented, which proved quite useful to meet the above-mentioned requirements. We discussed the merits and demerits of this new model which features two, a priori independent, phenomenological parameters in the definition (4.1) of the presymplectic (Lagrange) two-form σRS This flexibility enabled us to determine these adjustable parameters, the sought after model that would guarantee the BMT equations (in the weak field limit) with gyromagnetic ratio g, and provide the standard spin-orbit coefficient, proportional to g − 1, usually deduced from the DiracPauli equation in the quantum mechanical framework. After Raymond’s passing, I found it fair and useful to make accessible to our community one of his yet unanswered queries and to witness his great scientific insights
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