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


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.


Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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  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

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