On the origin of multi-component anyon wave functions

TL;DR

This paper explains how the multi-component structure of anyon wave functions originates from the gauge degrees of freedom in non-relativistic Chern-Simons theories, providing a theoretical understanding of their form.

Contribution

It demonstrates a singular gauge transformation that simplifies the Hamiltonian and clarifies the origin of multi-component wave functions in Chern-Simons theories.

Findings

Gauge transformation reduces Hamiltonian to free form

Finite-dimensional Hilbert space explains component structure

Provides theoretical insight into multi-component wave functions

Abstract

In this paper I discuss how the component structure of anyon wave functions arises in theories with non-relativistic matter coupled to a Chern-Simons gauge field on the torus. It is shown that there exists a singular gauge transformation which brings the Hamiltonian to free form. The gauge transformation removes a degree of freedom from the Hamiltonian. This degree of freedom generates only a finite dimensional Hilbert space and is responsible for the component structure of free anyon wave functions. This gives an understanding of the need for multiple component anyon wave functions from the point of view of Chern-Simons theory.