Skip to main content
SpringerLink
Log in

Braid Group Structure in Chern-Simons Theory on a Torus

  • Chapter
Contemporary Topics in Medium Energy Physics

  • 74 Accesses

Abstract

In recent years there has been an intense interest in the theory of anyons, particles obeying fractional statistics in 1 + 2 dimensions[1]. This is so not only because the theory itself exhibits very interesting mathematical structures, but also because it could be of relevance to some condensed matter systems, notably the fractional quantum Hall effect [2] and the high T c , superconductivity[3].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.M. Leinaas and J. Myrheim, Nuovo Cimento 37B (1977) 1;

    Google Scholar 

  2. G.A. Goldin, R. Menikoff, and D.H. Sharp, J. Math. Phys. 22 (1981) 1664; F. Wilczek, Phys. Rev. Lett. 48 (1982) 1144; ibid. 49 (1982) 957.

    Article  Google Scholar 

  3. R.B. Laughlin, Phys. Rev. Lett. 50 (1983) 1395;

    Google Scholar 

  4. B.I. Halperin, Phys. Rev. Lett. 52 (1984) 1583;

    Google Scholar 

  5. D. Arovas, R. Schrieffer and F. Wilczek, Phys. Rev. Lett. 53 (1984) 722; R. Tao and Y-S. Wu, Phys. Rev. B31 (1985) 6859.

    Article  MathSciNet  Google Scholar 

  6. V. Kalmeyer and R. B. Laughlin, Phys. Rev. Lett. 59 (1987) 2095; R. B. Laughlin, Science 242 (1988) 525;

    Article  Google Scholar 

  7. R. B. Laughlin, Phys. Rev. Lett. 60 (1988) 2677.

    Google Scholar 

  8. J. Schonfeld, Nucl. Phys. B185 (1981) 157;

    Article  ADS  Google Scholar 

  9. R. Jackiw and S. Templeton, Phys. Rev. D23 (1981) 2291;

    ADS  Google Scholar 

  10. S. Deser, R. Jackiw, and S. Templeton, Phys. Rev. Lett. 48 (1982) 975; Ann. Phys. (N.Y.) 140 (1982) 372; 185 (1988) 406 (E);

    Google Scholar 

  11. C.R. Hagen, Ann. Phys. (N. Y.) 157 (1984) 342; Phys. Rev. D31 (1985) 2135.

    Google Scholar 

  12. Y. Hosotani, Phys. Rev. Lett. 62 (1989) 2785; Phys. Rev. Lett. 64 (1990) 1691.

    Google Scholar 

  13. D.J. Thouless and Y.S. Wu, Phys. Rev. B31 (1985) 1191;

    Article  MathSciNet  ADS  Google Scholar 

  14. K. Lee, Boston Univ. report, Anyons on spheres and tori,BU/HEP-89–28;

    Google Scholar 

  15. A.P. Polychronakos, Ann. Phys. (N. Y.) 203 (1990) 231; Univ. of Florida preprint, Abelian Chern-Simons theories and conformal blocks UFIFT-HEP89–9; Phys. Lett. 241B (1990) 37;

    MathSciNet  Google Scholar 

  16. A. Comtet, J. McCabe and S. Ouvry, IPN preprint, Some remarks on anyons on the 2-sphere (to appear in Phys. Rev. D (1992).

    Google Scholar 

  17. S. Elitzur, G. Moore, A. Schwimmer and N. Seiberg, Nucl. Phys. B326 (1989) 108;

    Article  MathSciNet  ADS  Google Scholar 

  18. M. Bos and V.P. Nair, Phys. Lett. 223B (1989) 61; Int. J. Mod. Phys. A5 (1990) 959;

    Article  MathSciNet  ADS  Google Scholar 

  19. J.M.F. Labastida and A.V. Ramallo, Phys. Lett. 227B (1989) 92; Phys. Lett. 228B (1989) 214;

    MathSciNet  Google Scholar 

  20. H. Murayama, Z. Phys. C48 (1990) 79.

    MathSciNet  Google Scholar 

  21. E. Witten, Comm. Math. Phys. 121 (1989) 351.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. E. Fradkin, Phys. Rev. Lett,. 63 (1989) 322.

    Article  MathSciNet  ADS  Google Scholar 

  23. T. Einarsson, Phys. Rev. Lett. 64 (1990) 1995; Göteberg preprint, Fractional statistics on compact surfaces, ITP-91–1 (1991).

    Google Scholar 

  24. G.C. Segre, Pennsylvania preprint, A model of superconductivity.

    Google Scholar 

  25. S. Randjbar-Daemi, A. Salarn, and J. Strathdee, Phys. Lett. 240B (1990) 121.

    MathSciNet  Google Scholar 

  26. R. Iengo and K. Lechner, Nucl. Phys. B346 (1990) 551; Nucl. Phys. B364 (1991) 551.

    Article  MathSciNet  ADS  Google Scholar 

  27. G. Cristofano, G. Maiella, R. Musto and F. Nicodemi, Phys. Lett. 262B (1991) 88; Mod. Phys. Lett. A6 (1991) 1779.

    Google Scholar 

  28. X.G. Wen, E. Dagotto, and E. Fradkin, Phys. Rev. B42 (1990) 6110.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. S. Chakravarty and Y. Hosotani, Phys. Rev. D44 (1991) 441.

    ADS  Google Scholar 

  30. T.D. Imbo and J. March-Russell, Phys. Lett. 252B (1990) 84.

    MathSciNet  Google Scholar 

  31. Y.S. Wu, Y. Hatsugai, and M. Kohmoto, Phys. Rev. Lett. 66 (1991) 659; Phys. Rev. B43 (1991) 2661.

    Google Scholar 

  32. C.-L. Ho and Y. Hosotani, Int. J. Mod. Phys. A7 (1992) 5797.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. C.-L. Ho and Y. Hosotani, Minnesota preprint, Operator Algebra in ChernSimons Theory on a Torus,TPI-MINN-92/41-T (Sep 92).

    Google Scholar 

  34. E. Witten, Nucl. Phys. B258 (1985) 75; Y. Hosotani, Ann. Phys. (N.Y.) 190 (1989) 233.

    Article  ADS  Google Scholar 

  35. G.Date, T.R. Govindarajan, P. Sankaran and R. Shankar, Comm. Math. Phys. 132 (1990) 293.

    Article  MathSciNet  ADS  Google Scholar 

  36. X.G. Wen, Phys. Rev. B40 (1989) 7387; Int. J. Mod. Phys. B4 (1990) 239.

    Article  ADS  Google Scholar 

  37. K. Lechner, Trieste ISAS preprint, Anyon physics on the torus,thesis, (Apr. 91).

    Google Scholar 

  38. J.S. Birman, Comm. Pure and Applied Math. 22 (1969) 41.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Tamkang University, Tamsui, 25137, Taiwan, R.O.C.

    Choon-Lin Ho

  2. School of Physics and Astronomy, University of Minnesota Minneapolis, MN, 55455, USA

    Yutaka Hosotani

Authors
  1. Choon-Lin Ho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yutaka Hosotani
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Ruhr-Universität Bochum, Bochum, Germany

    Klaus Goeke

  2. National Taiwan University, Taipei, Taiwan

    W-Y. Pauchy Hwang

  3. Forschungszentrum Jülich and Universität Bonn, Bonn, Germany

    Josef Speth

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media New York

About this chapter

Cite this chapter

Ho, CL., Hosotani, Y. (1994). Braid Group Structure in Chern-Simons Theory on a Torus. In: Goeke, K., Hwang, WY.P., Speth, J. (eds) Contemporary Topics in Medium Energy Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9835-7_25

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-9835-7_25

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9837-1

  • Online ISBN: 978-1-4757-9835-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation