Anyons with anomalous gyromagnetic ratio and the Hall effect

AbstractLetting the mass depend on the spin-field coupling as M2=m2−(eg/2c2)FαβSαβ, 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 nonrelativistic 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