The statistics transmuting Chern-Simons field and the braid group on Riemann surfaces of genus g>0

TL;DR

This paper demonstrates that bosons interacting with an abelian Chern-Simons field on higher-genus Riemann surfaces can be transformed into free particles, revealing a deep connection with braid group representations and anyons.

Contribution

It generalizes the equivalence between bosons coupled to Chern-Simons fields and anyons from the plane to higher-genus Riemann surfaces using a singular gauge transformation.

Findings

Hamiltonian can be transformed to free form via singular gauge transformation

Wave functions form a multi-component braid group representation

Establishes equivalence of bosons with Chern-Simons fields and anyons on Riemann surfaces

Abstract

We study bosons interacting with an abelian Chern-Simons field on Riemann surfaces of genus $g>0$. It is shown that a singular gauge transformation brings the hamiltonian to free form. The transformed wave functions furnish a multi-component representation of the braid group studied by Imbo and March-Russell. The construction constitutes a proof of the equivalence of bosons coupled to a Chern-Simons field and anyons and generalizes the well known equivalence of the two pictures on the plane.