Some Simple (Integrable) Models of Fractional Statistics
Abstract
Description
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.
18 pages, Latex. Two lectures presented at 1994 Les Houches Summer School ``Fluctuating Geometries in Statistical Mechanics and Field Theory'' (also available at http://xxx.lanl.gov/lh94/ )
18 pages, Latex. Two lectures presented at 1994 Les Houches Summer School ``Fluctuating Geometries in Statistical Mechanics and Field Theory'' (also available at http://xxx.lanl.gov/lh94/ )