A geometrical particle model for anyons

TL;DR

This paper introduces a geometrical particle model based on light-like curves in (2+1) dimensions, which upon quantization produces the anyonic field equation with a specific mass-spin relation.

Contribution

It presents a novel geometrical model for anyons that links light-like curves to quantum anyonic fields and derives a unique mass-spin relation.

Findings

Quantization of the model yields the (2+1)-dimensional anyonic field equation.

The model establishes a relation between mass and spin: mass times spin equals the square of the coupling constant.

The approach connects geometrical particle models with quantum field theory for anyons.

Abstract

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., $mass \times spin =\alpha^2$, with $\alpha$ the coupling constant in front of the action.