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.
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