Turning Bosons into Fermions: Exclusion Statistics, Fractional Statistics and the Simple Harmonic Oscillator

TL;DR

This paper constructs operators for generalized particles called g-ons based on bosonic algebra, revealing their connection to exclusion and fractional statistics through symmetry breaking linked to the braid group.

Contribution

It introduces a novel algebraic framework for g-ons, connecting exclusion statistics with fractional statistics via symmetry considerations.

Findings

g-ons are derived from bosonic algebra through symmetry breaking

Link established between exclusion and fractional statistics

Demonstrates the role of braid group symmetry in particle statistics

Abstract

Motivated by Haldane's exclusion statistics, we construct creation and annihilation operators for $g$-ons using a bosonic algebra. We find that $g$-ons appear due to the breaking of a descrete symmetry of the original bosonic system. This symmetry is intimately related to the braid group and we demonstrate a link between exclusion statistics and fractional statistics.