Deformation quantization of compact Kähler manifolds by Berezin-Toeplitz quantization


Schlichenmaier, Martin


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URL: http://ub-madoc.bib.uni-mannheim.de/1330
URN: urn:nbn:de:bsz:180-madoc-13308
Document Type: Working paper
Year of publication: 2000
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Keywords (English): quantization , Kähler manifolds , star-products , semi-classical limit , Toeplitz structure
Abstract: For arbitrary compact quantizable Kähler manifolds it is shown how a natural formal deformation quantization (star product) can be obtained via Berezin-Toeplitz operators. Results on their semi-classical behaviour (their asymptotic expansion) due to Bordemann, Meinrenken and Schlichenmaier are used in an essential manner. It is shown that the star product is null on constants and fulfills parity. A trace is constructed and the relation to deformation quantization by geometric quantization is given.
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Das Dokument wird vom Publikationsserver der Universitätsbibliothek Mannheim bereitgestellt.




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Schlichenmaier, Martin (2000) Deformation quantization of compact Kähler manifolds by Berezin-Toeplitz quantization. Open Access [Working paper]
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