A Geometrical Particle Model for Anyons

We consider the simplest geometrical particle model associated with light-like curves in (2+1) dimensions. The action is proportional to the pseudo-arc length of the particle's path. We show that under quantization, it yields the (2+1)-dimensional anyonic field equation supplemented with a Majorana-like relation on mass and spin, i.e. mass × spin =α 2 , with α the coupling constant in front of the action.