Dualities in fractional statistics

TL;DR

This paper simplifies the derivation of Haldane fractional statistics at thermal equilibrium and reveals a duality invariance in the mean occupation number under a nonabelian subgroup of fractional linear transformations.

Contribution

It introduces a simplified derivation of fractional statistics and uncovers a novel duality invariance property of the mean occupation number.

Findings

Simplified derivation of Haldane fractional statistics.

Identification of a duality invariance in the mean occupation number.

Invariance under a nonabelian subgroup of fractional linear transformations.

Abstract

We first reobtain in a simpler way the Haldane fractional statistics at thermal equilibrium using an interpolation argument. We then show that the mean occupation number for fractional statistics is invariant to a group of duality transformations, a nonabelian subgroup of the fractional linear group