Normalized Weyl-type *-product on Kähler manifolds

  • Takuya Masuda


A new kind of mathematics is thought necessary for a non-perturbative description of the string theory just as Riemannian geometry is indespensable for the description of the theory of general relativity. Non-commutative geometry is one of the strong candidate for it.




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Maxim Kontsevich, “Deformation quantization of Poisson manifolds”, q- alg/9709040.Google Scholar
  2. [2]
    Alberto S. Cattaneo and Giovanni Felder, “A path integral approach to the Kontsevich quantization formula, Commun”.Math.Phys. 212, 2000, 591–611.MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3]
    J. E. Moyal, Proc. Cambridge. Phil. Soc. 45, 1949, 99.MathSciNetMATHGoogle Scholar
  4. [4]
    H. J. Groenewold, Physica, 12, 1946, 405–60.MathSciNetADSMATHCrossRefGoogle Scholar
  5. [5]
    Michel Cahen, Simone Gutt and John Rawnsley, Trans. AMS, 337, 1993, 73–98MATHGoogle Scholar
  6. [6]
    Alexander V. Karabegov, Comm. Math. Phys., 180, 1996, 745–755MATHCrossRefGoogle Scholar
  7. Nicolai Reshetikhin and Leon A. Takhtajan, “Deformation Quantization of Kähler Manifolds”, math.QA/9907171.Google Scholar
  8. [8]
    Satoru Saito and Kazunori Wakatsuki, “Symmetrization of Berezin Star Prod- uct and Path Integral Quantization”, hep-th/9912265, Prog. Theor. Phys. 104 No.5, 2000.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Takuya Masuda
    • 1
  1. 1.Department of PhysicsTokyo Metropolitan UniversityTokyoJapan

Personalised recommendations