Berezin-Toeplitz Quantization and Berezin Transform

Schlichenmaier, Martin

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URN: urn:nbn:de:bsz:180-madoc-16029
Document Type: Working paper
Year of publication: 2000
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
Subject headings (SWD): Berezin-Transformation , Toeplitz-Form , Fubini-Study-Metrik
Abstract: In this lecture results on the Berezin-Toeplitz quantization of arbitrary compact quantizable Kähler manifolds are presented. These results are obtained in joint work with M. Bordemann and E. Meinrenken. The existence of the Berezin-Toeplitz deformation quantization is also covered. Recent results obtained in joint work with A. Karabegov on the asymptotic expansion of the Berezin transform for arbitrary quantizable compact Kähler manifolds are explained. As an application the asymptotic expansion of the Fubini-Study fundamental form under the coherent state embedding is considered. Some comments on the dynamics of the quantum operators are given. (This is an extended write-up of an invited lecture presented at the workshop "Asymptotic properties of time evolutions in classical and quantum systems", September 13-17, 1999, Bologna, Italy.)
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