Anyons with anomalous gyromagnetic ratio & the Hall effect C . Duval

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 = 2, the only allowed motions are those which satisfy the Hall law. For each g = 2, 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 twofold central extension of the planar Galilei group.