## Fractional Statistics and Anyon SuperconductivityThe occurrence of fractional statistics has been discovered in more and more quantum field theory models, including some of the most geometrical and canonical ones. In a remarkable case, the fractional quantum statistics of quasiparticles in the fractional quantized Hall effect (FQHE) contributes to the understanding of states found there. Very recent work has indicated that similar possibilities arise for two-dimensional films in certain states of liquid 3He. Perhaps most exciting, although quite speculative at this moment, are recent attempts to apply fractional statistics to spin systems, and specifically to the behaviour of the 2-dimensional copper oxide layers that seem to be critical to the phenomenon of high-temperature superconductivity. It has recently been shown that fractional statistics automatically implies superconductivity of a qualitatively new kind. This collection of reprints with comprehensive commentary will serve as a valuable reference for those interested in the subject but have found it difficult to acquire basic knowledge, or a coherent view of the whole, due to the scattered literature available at present. |

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### Contents

Transmutation and Fractionization of Angular Momentum | 4 |

Trajectory Space and the Braid Group | 11 |

Fictitious Field Construction and Quantum Mechanical Examples | 17 |

AharonovB6hm Scattering and its Implications | 21 |

HopfTerm | 27 |

Local Field Theory ChernSimons Construction | 34 |

Berry Phase and Anyons in the Quantized Hall Effect | 40 |

Induced Quantum Numbers | 47 |

PartHL REPRINTED PAPERS | 103 |

Classics | 105 |

Finkelstein and J Rubinstein Connection between Spin Statistics and Kinks J Math Phys 9 1968 17621779 | 107 |

Y Aharonov and D B6hm Significance of Electromagnetic Potentials in the Quantum Theory Phys Rev 115 1959 485491 | 115 |

Lcinaas and J Myrhcim On the Theory of Identical Particles Nuovo Cimento 37 1977 123 | 132 |

Phys Rev Lett 48 1982 11441146 | 155 |

The Last Bastion of Rationality | 157 |

J Goldstone and F Wilczek Fractional Quantum Numbers on Solitons Phys Rev Lett 471981986989 | 159 |

Boundary and Coboundary | 50 |

Part H STATES OF ANYON MATTER | 57 |

Definition of Anyons | 60 |

Average Field Theory | 62 |

Basic Mechanism | 65 |

Phenomenology | 72 |

Adiabatic Principle | 80 |

More Superconducting States | 82 |

Quantized Hall States | 83 |

Anyon Metal | 87 |

Microscopic Origins | 89 |

Conclusions | 98 |

Phys Rev Lett 491982957959 | 166 |

Y S Wu General Theory for Quantum Statistics in Two Dimensions | 183 |

A S Goldhaber and R Mackenzie Are Cyons Really Anyons? | 200 |

Polyakov FermiBose Transmutations Induced by Gauge Fields | 214 |

Oblique Confinement and the Fractional Quantum Hall Effect | 247 |

Anyons in the Quantized Hall Effect | 249 |

Arovas J R Schrieffer and F Wilczek Fractional Statistics and | 256 |

Chiral Spin States | 307 |

Anyon Superconductivity | 325 |

Fetter C B Hanna and R B Laughlin RandomPhase Approximation | 339 |

Y H Chen F Wilczek E Witten and B I Halperin On Anyon | 409 |

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