分数统计与量子理论（英文版）

    Sometime in early 1994, I received a letter from World Scientific, Singapore, inviting me to write a book on anyons. That made me think about the whole thing. Initially I was not sure if I should spend about two years of my research career in such a venture. At that time I went through the literature on this field and I had a careful look at the only monograph on this subject by Lerda as well as the book on anyon superconductivity edited by Wilczek. While I liked parts of these books (and their influence is apparent in parts of the book), I also felt that our perceptions are some what different. Having worked on both the non-relativistic as well as the relativistic anyon models, I was finally convinced that perhaps the time had come to accept this opportunity and put forward my point of view and hence this book.

Sometime in early 1994, I received a letter from World Scientific, Singapore, inviting me to write a book on anyons. That made me think about the whole thing. Initially I was not sure if I should spend about two years of my research career in such a venture. At that time I went through the literature on this field and I had a careful look at the only monograph on this subject by Lerda as well as the book on anyon superconductivity edited by Wilczek. While I liked parts of these books (and their influence is apparent in parts of the book), I also felt that our perceptions are some what different. Having worked on both the non-relativistic as well as the relativistic anyon models, I was finally convinced that perhaps the time had come to accept this opportunity and put forward my point of view and hence this book.

　　本书为英文版。

1. Introduction
1.1 Historical Review
1.2 Plan of the Book
2 Fractional Statistics in Two Dimensions
2.1 Introduction
2.2 Why Fractional Spin?
2.3 Wily Fractional Statistics?
2.4 Basic Properties of Anyons
2.5 Flux Tube Model of Anyons
2.6 The Braid Group
3 Quantum Mechanics of Anyons
3.1 Introduction
3.2 Two Noninteracting Anyons
3.3 Two Anyons in an Oscillator Potential
3.4 Two Anyons in a Uniform Magnetic Field
3.5 Magnetic Field with Coulomb Repulsion
3.6 Scattering of Two Anyons in Coulomb Field
3.7 N Anyons in an Oscillator Potential
3.8 Three Anyon Ground State
3.9 General Results for N Anyons
3.10 N Anyons Experiencing a N-body Potential
3.11 N Anyons in a Uniform Magnetic Field
3.12 Pseudo-Integrability of N Anyon systen
4 Statistical Mechanics of an Ideal Anyon Gas
4.1 Introduction
4.2 Idel Fermi Gas in Two Dimensions
4.3 Ideal Bose Gas in Two Dimensions
4.4 Ideal Anyon Gas: Second Virial Coefficient
4.5 Ideal Anyon Gas: Third Virial Coefficient
4.6 Ideal Anyon Gas: Higher Virial Coefficient
5 Fractional Exclusion Statistics
5.1 Introducion
5.2 Distributin Function
5.3 Thermodynamics of an Ideal Gas
5.4 Gentile Statistics
5.5 New Fractional Exclusion Statistics
6 introdcuion to Chern-Simons Term
6.1 Introcution
6.2 What is Chern-Simons Term?
6.3 Gauge Invariant Mass Term?
6.4 Behavior Under c, p, and T
6.5 Coleman-Hill Theorem
……
7 Soliton as Anyon in Field Theories
8 Anyons as Elementary Field Quanta
9 Anyon Superconductivity
10 Quantum Hall Effect and Anyons
11 Omitted Topics