Abstract
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→∞.
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Communicated by A. Jaffe
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Bordemann, M., Meinrenken, E. & Schlichenmaier, M. Toeplitz quantization of Kähler manifolds anggl(N), N→∞ limits. Commun.Math. Phys. 165, 281–296 (1994). https://doi.org/10.1007/BF02099772
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DOI: https://doi.org/10.1007/BF02099772