Communications in Mathematical Physics

, Volume 165, Issue 2, pp 281–296 | Cite as

Toeplitz quantization of Kähler manifolds anggl(N), N→∞ limits

  • Martin Bordemann
  • Eckhard Meinrenken
  • Martin Schlichenmaier


For general compact Kähler manifolds it is shown that both Toeplitz quantization and geometric quantization lead to a well-defined (by operator norm estimates) classical limit. This generalizes earlier results of teh authors and Klimek and Lesniewski obtained for the tours and higher genus Riemann surfaces, respectively. We thereby arrive at an approximation of the Poisson algebra by a sequence of finitedimensional matrix algebrasgl(N), N→∞.


Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Martin Bordemann
    • 1
  • Eckhard Meinrenken
    • 2
  • Martin Schlichenmaier
    • 3
  1. 1.Department of PhysicsUniversity of FreiburgFreiburgGermany
  2. 2.Department of MathematicsM.I.T.CambridgeUSA
  3. 3.Department of Mathematics and computer ScienceUniverseity of MannheimMannheimGermany

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