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

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.

10 pages, ReVTeX 3.0

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Cited by in corpus (5)

• Statistical correlations in an ideal gas of particles obeying fractional exclusion statistics
• Exclusion statistics,operator algebras and Fock space representations
• Statistical correlations of an anyon liquid at low temperatures
• Many-body constraints and non-thermal behavior in 1D open systems with Haldane exclusion statistics
• Generalized exclusion and Hopf algebras