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Anyons with anomalous gyromagnetic ratio & the Hall effect

C. Duval·P. A. Horvathy
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Abstract

Letting the mass depend on the spin-field coupling as $M^2=m^2-(eg/2c^2)F_{αβ}S^{αβ}$, we propose a new set of relativistic planar equations of motion for spinning anyons. Our model can accommodate any gyromagnetic ratio $g$ and provides us with a novel version of the Bargmann-Michel-Telegdi equations in 2+1 dimensions. The system becomes singular when the field takes a critical value, and, for $g\neq2$, the only allowed motions are those which satisfy the Hall law. For each $g\neq2,0$ a secondary Hall effect arises also for another critical value of the field. The non-relativistic limit of our equations yields new models which generalize our previous ``exotic'' model, associated with the two-fold central extension of the planar Galilei group.

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C. Duval, P. A. Horvathy. 2004-07-02. Anyons with anomalous gyromagnetic ratio & the Hall effect. https://doi.org/10.1016/j.physletb.2004.05.049

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