Anyons on Higher Genus Surfaces - a Constructive Approach

TL;DR

This paper presents a constructive method for modeling anyons on higher genus surfaces by embedding them in three-dimensional space, explicitly deriving braid group representations and analyzing their spin-statistics relation.

Contribution

It introduces a concrete 3D flux tube model for anyons on complex surfaces and derives their braid group representations explicitly.

Findings

Derived all representations of the spinning braid group for higher genus surfaces.

Showed that flux tube winding around handles influences wave function structure.

Argued that the anyons satisfy a generalized spin-statistics relation.

Abstract

We reconsider the problem of anyons on higher genus surfaces by embedding them in three dimensional space. From a concrete realization based on three dimensional flux tubes bound to charges moving on the surface, we explicitly derive all the representations of the spinning braid group. The component structure of the wave functions arises from winding the flux tubes around the handles. We also argue that the anyons in our construction must fulfil the generalized spin-statistics relation.