Advertisement

Communications in Mathematical Physics

, Volume 180, Issue 3, pp 745–755 | Cite as

Deformation quantizations with separation of variables on a Kähler manifold

  • Alexander V. Karabegov
Article

Abstract

We give a simple geometric description of all formal differentiable deformation quantizations on a Kähler manifoldM such that for each open subsetUM ⋆-multiplication from the left by a holomorphic function and from the right by an antiholomorphic function onU coincides with the pointwise multiplication by these functions. We show that these quantizations are in 1-1 correspondence with the formal deformations of the original Kähler metrics onM.

Keywords

Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., Sternheimer, D.: Deformation theory and quantization. Ann. Phys.111, 1–151 (1978)Google Scholar
  2. 2.
    Berezin, F.A.: Quantization. Math. USSR Izv.8, 1109–1165 (1974)Google Scholar
  3. 3.
    Cahen, M., Gutt, S., Rawnsley, J.: Quantization of Kähler manifolds, II. Trans. Am. Math. Soc.337, 73–98 (1993)Google Scholar
  4. 4.
    Cahen, M., Gutt, S., Rawnsley, J.: Quantization of Kähler manifolds, IV. Lett. Math. Phys.34, 159–168 (1995)Google Scholar
  5. 5.
    Karabegov, A.V.: On deformation quantization on a Kähler manifold associated to Berezin's quantization. To appear in Funct. Anal. Appl.Google Scholar
  6. 6.
    Moreno, C.: *-products on some Kähler manifolds. Lett. Math. Phys.11, 361–372 (1986)Google Scholar
  7. 7.
    Moreno, C.: Invariant star products and representations of compact semisimple Lie groups. Lett. Math. Phys.12, 217–229 (1986)Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Alexander V. Karabegov
    • 1
  1. 1.Joint Institute for Nuclear ResearchDubnaRussia

Personalised recommendations