Toeplitz Quantization of Kähler Manifolds and gl(N), N → ∞

Bordemann, Martin ; Meinrenken, Eckhard ; Schlichenmaier, Martin

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URN: urn:nbn:de:bsz:180-madoc-13174
Document Type: Working paper
Year of publication: 1993
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
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 the authors and Klimek and Lesniewski obtained for the torus and higher genus Riemann surfaces, respectively. We thereby arrive at an approximation of the Poisson algebra by a sequence of finite-dimensional matrix algebras gl(N), N → ∞.
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