Spin Transmutation in (2+1) Dimensions

TL;DR

This paper investigates how the spin of particles in a (2+1)-dimensional relativistic anyon model can be continuously transmuted through Chern-Simons gauge interactions, revealing equivalences among various models.

Contribution

It demonstrates spin-statistics transmutation using a random walk approach and shows how certain gauge parameters can be absorbed into particle spin, establishing model equivalences.

Findings

Spin and statistics transmutation demonstrated.

Integer or half-integer parts of the statistical parameter absorbed into spin.

Large class of models shown to be equivalent for given parameters.

Abstract

We study a relativistic anyon model with a spin-$j$ matter field minimally coupled to a statistical gauge potential governed by the Chern-Simons dynamics with a statistical parameter $\alpha$. A spin and statistics transmutation is shown in terms of a continuous random walk method. An integer or odd-half-integer part of $\alpha$ can be reabsorbed by change of $j$. We discuss the equivalence of a large class of (infinite number) Chern-Simons matter models for given $j$ and $\alpha$.