Communications in Mathematical Physics

, Volume 145, Issue 1, pp 1–16 | Cite as

Quantization ofSL(2,R) Chern-Simons theory

  • T. P. Killingback
Article

Abstract

We discuss Chern-Simons gauge theory with anSL(2,R) gauge group on an arbitrary 3-manifoldM. TheSL(2,R) Chern-Simons action is defined for gauge bundles overM of arbitrary topological type. The geometric quantization ofSL(2,R) Chern-Simons theory is discussed and related to the quantization of Teichmüller space. The generalization to Chern-Simons theory with anSL(n,R) gauge group is also considered.

Keywords

Neural Network Statistical Physic Complex System Gauge Theory Nonlinear Dynamics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Witten, E.: Commun. Math. Phys.117, 353 (1988)Google Scholar
  2. 2.
    Witten, E.: Commun. Math. Phys.118, 411 (1988)Google Scholar
  3. 3.
    Witten, E.: Commun. Math. Phys.121, 351 (1989)Google Scholar
  4. 4.
    Killingback, T. P.: Phys. Lett.B219, 448 (1989)Google Scholar
  5. 5.
    Elitzur, S., Moore, G., Schwimmer, A., Seiberg, N.: IAS preprint IASSNS-HEP-89/20 (1989); Dunne, G., Jackiw, R., Trugenberger, C.: MIT preprint MIT-CUP-1711 (1989); Bos, M., Nair, V.: Columbia preprint CU-TP-432 (1989); Murayama, H.: TTokyo preprint (1989)Google Scholar
  6. 6.
    Verlinde, E., Verlinde, H.: IAS preprint IASSNS-HEP-89/58 (1989)Google Scholar
  7. 7.
    Witten, E.: Nucl. Phys.B311, 46 (1989)Google Scholar
  8. 8.
    Witten, E.: IAS preprint IASSNS-HEP-89/65 (1989)Google Scholar
  9. 9.
    Killingback, T. P., Rees, E. G.: Class. Quantum Grav.4, 357 (1987)Google Scholar
  10. 10.
    Dijkgraaf, R., Witten, E.: IAS preprint IASSNS-HEP-89/33 (1989)Google Scholar
  11. 11.
    Killingback, T. P.: CERN preprint TH. 5699 (1990)Google Scholar
  12. 12.
    Husemoller, D.: Fibre bundles. Berlin, Heidelberg, New York: Springer 1996Google Scholar
  13. 13.
    Spanier, E.: Algebraic topology, Berlin, Heidelberg, New York: Springer 1996Google Scholar
  14. 14.
    Stong, R.: Notes on cobordism theory. Princeton, NJ: Princeton University Press 1968Google Scholar
  15. 15.
    Corner, P.: Differentiable periodic maps. Lecture Notes in Mathematics, vol. 738. Berlin, Heidelberg, New York: SpringerGoogle Scholar
  16. 16.
    Bos, M., Nair, V.: Phys. Lett.B223, 61 (1989)Google Scholar
  17. 17.
    Goldman, W.: Adv. Math.54, 200 (1984)Google Scholar
  18. 18.
    Milnor, J.: Commun. Math. Helv32, 16 (1957); Wood, J.: Commun. Math. Helv.51, 183 (1976)Google Scholar
  19. 19.
    Woodhouse, N.: Geometric quantization. Oxford: Oxford Universit Press 1980Google Scholar
  20. 20.
    Hitchin, N.: Proc. London Math. Soc.55, 59 (1987)Google Scholar
  21. 21.
    Hitchin, N., Karlhede, A., Lindström, U., Roček, M.: Commun. Math. Phys.108, 535 (1987)Google Scholar
  22. 22.
    Donaldson, S.: Proc. London Math. Soc.55, 509 (1987)Google Scholar
  23. 23.
    Friedan, D., Shenker, S.: Nucl. Phys.B281, 509 (1987)Google Scholar
  24. 24.
    Segal, G.: The definition of conformal field theory. (to appear)Google Scholar
  25. 25.
    Goldman, W.: Bull. A.M.S. (NS)6, 91 (1982)Google Scholar
  26. 26.
    Quillen, D.: Funct. Anal. Appl.19, 31 (1986); Bismut, J., Freed, D.: Commun. Math. Phys.106, 159 (1986);107, 10 (1986)Google Scholar
  27. 27.
    Verlinde, H.: Princeton preprint PUPT-89/1140 (1989)Google Scholar
  28. 28.
    Witten, E.: IAS preprint IASSN-HEP-89/38 (1989)Google Scholar
  29. 29.
    Wolpert, S.: Ann. Math.117, 207 (1983)Google Scholar
  30. 30.
    Jakobsen, H., Kac., V.: MIT preprint (1989)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • T. P. Killingback
    • 1
  1. 1.Theory DivisionCERNGeneva 23Switzerland

Personalised recommendations