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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 researchers with a reasonable background in quantum and statistical mechanics.
Topics in the first part of the book include the flux tube model of anyons, the braid group and a detailed discussion about the various aspects of quantum and statistical mechanics of a noninteracting anyon gas.
The second part of the book includes 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.
Since the publication of the first edition of the book, an exciting possibility has emerged, that of quantum computing using anyons. A section has therefore been included on this topic in the second edition. In addition, new sections have been added about scattering of anyons with hard disk repulsion as well as fractional exclusion statistics and negative probabilities.
Sample Chapter(s)
Chapter 1: Introduction (676 KB)
Contents:
- Fractional Statistics in Two Dimensions
- Quantum Mechanics of Anyons
- Statistical Mechanics of an Ideal Anyon Gas
- Fractional Exclusion Statistics
- Introduction to the Chern–Simons Term
- Soliton as Anyon in Field Theories
- Anyons as Elementary Field Quanta
- Anyon Superconductivity
- Quantum Hall Effect and Anyons
- Omitted Topics
Readership: Condensed matter physicists, mathematical physicists and materials scientists.
