Fractional Statistics and Quantum Theory

This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book include the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about fractional statistics from the point of view of Chern-Simons theories. Topics covered here include Chern-Simons field theories, charged vortices, anyon superconductivity and the fractional quantum Hall effect. A chapter will also be devoted to the recent topic of fractional exclusion statistics and the concepts will be illustrated with the example of the Calogero-Sutherland model.