Chern-Simons Gauge Theory and Spin-Statistics Connection in 2 Dimensional Quantum Mechanics

  • G. W. Semenoff
Part of the NATO ASI Series book series (NSSB, volume 238)

Abstract

It has been known for some time that the possibilities for quantum statistics in 1 and 2 space dimensions are more general than in the familiar 3 dimensional world. There has recently been much interest in the 2 dimensional case where, besides the usual Bosons and Fermions there can be particles with intermediate statistics.

Keywords

Vortex Soliton 

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References

  1. 1.
    B. Halperin, Phys. Rev. Lett. 52 (1984), 1583.ADSCrossRefGoogle Scholar
  2. R. Laughlin, Phys. Rev. Lett. 50 (1983), 1395.ADSCrossRefGoogle Scholar
  3. T.H.Hansson, S.Kivelson and Zhang, Phys. Rev.Lett. 62 (1989), 82.ADSCrossRefGoogle Scholar
  4. S.Girvin in The Quantum Hall Effect,ed. by R. Prange and S. Girvin, Springer-Verlag 1987.Google Scholar
  5. G. W. Semenoff and P. Sodano. Phys. Rev. Lett. 57 (1986).Google Scholar
  6. 2.
    V.Kalmeyer and R.B.Laughlin, Phys.Rev.Lett. 59 (1987), 2095.ADSCrossRefGoogle Scholar
  7. R. B. Laughlin, Phys. Rev. Lett. 60 (1988), 2677.Google Scholar
  8. A. L. Fetter, C. B. Hanna and R. B. Laughlin, Phys.Rev. B39 (1989), 9679.ADSGoogle Scholar
  9. T. Banks and J. Lykken, Santa Cruz preprint, 1989.Google Scholar
  10. 3.
    T.H.R. Skyrme, Proc. Roy. Soc. Lond. A260 (1961), 127.MathSciNetADSMATHCrossRefGoogle Scholar
  11. D. Finkelstein, Jour. Math. Phys. 7 (1966), 1218.MathSciNetADSMATHCrossRefGoogle Scholar
  12. D. Finkelstein and J. Rubenstein, Jour. Math. Phys. 9 (1968).Google Scholar
  13. 4.
    C.M. De Witt and Laidlaw, Phys. Rev. D3 (1971), 1375.Google Scholar
  14. 5.
    S. Coleman, Phys. Rev. D11 (1975), 2088.Google Scholar
  15. S. Mandelstam, Phys. Rev. D11 (1975), 3026.MathSciNetADSGoogle Scholar
  16. 6.
    J. Leinaas and J. Myrlheim, Nuovo Cimento B37 (1977), 1.ADSGoogle Scholar
  17. 7.
    W.Siegel, Nucl.Phys. B156, 135 (1979).ADSCrossRefGoogle Scholar
  18. J. Shonfeld, Nucl. Phys. D185 (1981), 157.ADSCrossRefGoogle Scholar
  19. R. Jackiw and S. Templeton, Phys. Rev. D24 (1981), 2291.Google Scholar
  20. 8.
    S. Deser, R. Jackiw and S. Templeton, Phys. Rev. Lett. 48 (1982), 475.ADSCrossRefGoogle Scholar
  21. Ann. Phys. (N. Y.)140 (1982), 372.Google Scholar
  22. 9.
    A.S. Schwarz, Lett. Math. Phys. 2 (1978), 247.ADSMATHCrossRefGoogle Scholar
  23. 10.
    Y. Akutsu and M. Wadati, J. Phys. Soc. Japan 56 (1987), 3039.MathSciNetADSMATHCrossRefGoogle Scholar
  24. J. Phys. Soc. Japan 59 (1987), 3034.Google Scholar
  25. Y. Akutsu, T. Deguchi and M. Wadati, J. Phys. Soc. Japan 56 (1987), 3464.MathSciNetADSMATHCrossRefGoogle Scholar
  26. 11.
    E. Witten, Comm. Math. Phys. 121 (1989), 351.MathSciNetADSMATHCrossRefGoogle Scholar
  27. 12.
    F. Wilczek and A. Zee, Phys. Rev. Lett. 51 (1984), 2250.Google Scholar
  28. 13.
    Yong-Shi Wu, Phys. Rev. Lett. 52 (1984), 2103.MathSciNetADSCrossRefGoogle Scholar
  29. Yong-Shi Wu, Phys. Rev. Lett. 53 (1984), 111.MathSciNetADSCrossRefGoogle Scholar
  30. 14.
    A. M. Polyakov, Mod. Phys. Lett. A3 (1988), 325.Google Scholar
  31. 15.
    G. W. Semenoff, Phys. Rev. Lett. 61 (1988), 517.MathSciNetADSCrossRefGoogle Scholar
  32. 16.
    G. W. Semenoff and P. Sodano, Nucl. Phys. B328 (1989), 753.MathSciNetADSCrossRefGoogle Scholar
  33. 16.
    G. W. Semenoff and P. Sodano, Nucl. Phys. B328 (1989), 753.MathSciNetADSCrossRefGoogle Scholar
  34. 18.
    For a review of their work see J. Frohlich and P Marchetti, this preceedings.Google Scholar
  35. 19.
    R. Fox and L. Neuwirth, Math. Scand. 10 (1961), 119.MathSciNetGoogle Scholar
  36. E. Fadell and J. Van Buskirk, Duke Math. 29 (1962), 243.MathSciNetMATHCrossRefGoogle Scholar
  37. E. Artin, Ann. Math. 48 (1947), 101.MathSciNetMATHCrossRefGoogle Scholar
  38. 20.
    G.Semenoff, P.Sodano and Y.-S. Wu, Phys.Rev.Lett. 62 (1989).Google Scholar
  39. 21.
    S. Coleman and B. Hill, Phys. Lett. 159B (1985) 184.Google Scholar
  40. Y. Kao and M. Suzuki, Phys. Rev. D31 (1985), 2137.Google Scholar
  41. M. Bernstein and T. Lee, Phys. Rev. D32 (1985), 1020.Google Scholar
  42. 22.
    P. A. M. Dirac, Lectures on Quantum Mechanics, Yeshiva Press, New York, 1969.Google Scholar
  43. 23.
    P. W. Anderson, S. John, G. Baskaran, B. Doucot and S.-D. Liang, Princeton preprint 1988.Google Scholar
  44. E.J. Mele and D. Morse, Philadelphia Preprint, 1989.Google Scholar
  45. J. Ambjorn and G.W. Semenoff, Phys.Lett. B226 (1989), 107.MathSciNetGoogle Scholar
  46. E. Fradkin, Urbana preprint, 1989.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • G. W. Semenoff
    • 1
  1. 1.Department of PhysicsUniversity of British ColumbiaVancouverCanada

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