The Spin pp 61-69 | Cite as

New Kinds of Quantum Statistics

  • Frank Wilczek
Part of the Progress in Mathematical Physics book series (PMP, volume 55)


I review the quantum kinematics of identical particles, which suggests new possibilities, beyond bosons and fermions, in 2+1 dimensions; and how simple flux-charge constructions embody the new possibilities, leading to both abelian and nonabelian anyons. I briefly allude to experimental realizations, and also advertise a spinor construction of nonabelian statistics, that has a 3+1 dimensional extension.


Braid Group Identical Particle Fractional Quantum Abelian Case Superselection Sector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. M. Leinaas and J. Myrheim, Nuovo Cimento B37 (1977), 1.Google Scholar
  2. [2]
    R. Doplicher, R. Haag, and J. Roberts, Comm. Math. Phys. 35 (1972), 49.CrossRefADSMathSciNetGoogle Scholar
  3. [3]
    G. Goldin, R. Menikoff, and D. Sharp, J. Math. Phys. 22 (1981), 1664.CrossRefADSMathSciNetGoogle Scholar
  4. [4]
    F. Wilczek, Phys. Rev. Lett. 48 (1982), 1144; ibid. (1982), 1146; ibid. 49(1982), 957.CrossRefADSMathSciNetGoogle Scholar
  5. [5]
    F. Wilczek and A. Zee, Phys. Rev. Lett. 51 (1983), 2250; D. Arovas, J. R. Schrieffer, F. Wilczek, and A Zee Nucl. Phys. B251 [FS 13] (1985), 917.CrossRefADSMathSciNetGoogle Scholar
  6. [6]
    D. Arovas, J. R. Schrieffer and F. Wilczek, Phys. Rev. Lett. 53 (1984), 722.CrossRefADSGoogle Scholar
  7. [7]
    B. Halperin, Phys. Rev. Lett. 52 (1984), 1583.CrossRefADSGoogle Scholar
  8. [8]
    V. Goldman, J. Liu and A. Zaslavsky, Phys. Rev. B71 (2005), 153303; F. Camino, F. Zhou, and V. Goldman Phys. Rev. Lett. 98 (2007), 076805.CrossRefGoogle Scholar
  9. [9]
    G. Moore and N. Read, Nucl. Phys. B360 (1991), 362.CrossRefADSMathSciNetGoogle Scholar
  10. [10]
    Y. Aharonov and D. Bohm, Phys. Rev. 115 (1959), 485.MATHCrossRefADSMathSciNetGoogle Scholar
  11. [11]
    See M. Dolev, M. Heiblum, V. Umansky, A. Stern, and D. Mahalu, Nature 452 (2008), 829; I. Radu, J. Miller, C. Marcus, M. Kastner, L. Pfeiffer, and K. West, Science 320 (2008), 899.CrossRefADSGoogle Scholar
  12. [13]
    C. Nayak and F. Wilczek, Nucl. Phys. B479 (1996), 529.MATHCrossRefADSMathSciNetGoogle Scholar
  13. [14]
    D. Ivanov, Phys. Rev. Lett. 86 (2001), 268.CrossRefADSGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Frank Wilczek
    • 1
  1. 1.Department of PhysicsMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations