Fractional Statistics and Anyon Superconductivity

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World Scientific, 1990 - Technology & Engineering - 447 pages
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The 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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