Some Simple (Integrable) Models of Fractional Statistics

Details Some Simple (Integrable) Models of Fractional Statistics Some Simple (Integrable) Models of Fractional Statistics

1994-11-02

arxiv.org/abs/hep-th/9411017v1

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, Latex. Two lectures presented at 1994 Les Houches Summer School ``Fluctuating Geometries in Statistical Mechanics an

Scientific paper

In the first part, we introduce the notion of fractional statistics in the sense of Haldane. We illustrate it on simple models related to anyon physics and to integrable models solvable by the Bethe ansatz. In the second part, we describe the properties of the long-range interacting spin chains. We describe its infinite dimensional symmetry, and we explain how the fractional statistics of its elementary excitations is an echo of this symmetry. In the third part, we review recent results on the Yangian representation theory which emerged from the study of the integrable long-range interacting models.

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