Advertisement

Theoretical and Mathematical Physics

, Volume 157, Issue 3, pp 1745–1759 | Cite as

Twistor quantization of loop spaces of compact Lie groups

  • A. G. Sergeev
Article
  • 51 Downloads

Abstract

We consider the problem of twistor quantization for the loop space ΩTG of a compact Lie group G. We show that this problem is solvable in the critical dimension.

Keywords

twistor quantization loop space Fock bundle affine algebra Goodman-Wallach action 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Goodman and N. R. Wallach, J. Reine Angew. Math., 347, 69–133 (1984).zbMATHMathSciNetGoogle Scholar
  2. 2.
    A. Pressley and G. Segal, Loop Groups, Clarendon Press, Oxford (1986).zbMATHGoogle Scholar
  3. 3.
    A. A. Kirillov, Elements of the Theory of Representations [in Russian], Nauka, Moscow (1978); English transl. prev. ed. (Grundlehren Math. Wiss., Vol. 220), Springer, Berlin (1976).Google Scholar
  4. 4.
    A. G. Sergeev, Kähler Geometry of Loop Spaces [in Russian], MNTsMO, Moscow (2001).Google Scholar
  5. 5.
    J. Mickelsson, Comm. Math. Phys., 112, 653–661 (1987).zbMATHCrossRefADSMathSciNetGoogle Scholar
  6. 6.
    J. Mickelsson, Current Algebras and Groups, Plenum, New York (1989).zbMATHGoogle Scholar
  7. 7.
    A. L. Onishchik and E. B. Vinberg, Seminar on Lie Groups and Algebraic Groups [in Russian], Nauka, Moscow (1988); English transl.: Lie Groups and Algebraic Groups, Springer, Berlin (1990).zbMATHGoogle Scholar
  8. 8.
    S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vols. 1 and 2, Wiley, New York (1996).Google Scholar
  9. 9.
    G. Segal, Comm. Math. Phys., 80, 301–342 (1981).zbMATHCrossRefADSMathSciNetGoogle Scholar
  10. 10.
    M. J. Bowick and A. Lahiri, J. Math. Phys., 29, 1979–1981 (1988).zbMATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© MAIK/Nauka 2008

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRASMoscowRussia

Personalised recommendations