Identification of Berezin-Toeplitz Deformation Quantization

Karabegov, Alexander V. ; Schlichenmaier, Martin

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URN: urn:nbn:de:bsz:180-madoc-15997
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
Abstract: We give a complete identification of the deformation quantization which was obtained from the Berezin- Toeplitz quantization on an arbitrary compact Kähler manifold. The deformation quantization with the opposite star-product proves to be a differential deformation quantization with separation of variables whose dassifying form is explicitly calculated. Its characteristic dass (which dassifies star-products up to equivalence) is obtained. The proof is based on the microlocal description of the Szegö kernel of a strictly pseudoconvex domain given by Boutet de Monvel and Sjöstrand.
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