Berezin-Toeplitz Quantization for Compact Kähler Manifolds. A Review of Results

This article is a review on Berezin-Toeplitz operator and Berezin-Toeplitz deformation quantization for compact quantizable Kähler manifolds. The basic objects, concepts, and results are given. This concerns the correct semiclassical limit behaviour of the operator quantization, the unique Berezin-T...

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Main Author: Martin Schlichenmaier
Format: Article
Language:English
Published: Wiley 2010-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2010/927280
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author Martin Schlichenmaier
author_facet Martin Schlichenmaier
author_sort Martin Schlichenmaier
collection DOAJ
description This article is a review on Berezin-Toeplitz operator and Berezin-Toeplitz deformation quantization for compact quantizable Kähler manifolds. The basic objects, concepts, and results are given. This concerns the correct semiclassical limit behaviour of the operator quantization, the unique Berezin-Toeplitz deformation quantization (star product), covariant and contravariant Berezin symbols, and Berezin transform. Other related objects and constructions are also discussed.
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spelling doaj-art-0376c8e4cd834e589ced58f4475125d22025-08-20T03:55:32ZengWileyAdvances in Mathematical Physics1687-91201687-91392010-01-01201010.1155/2010/927280927280Berezin-Toeplitz Quantization for Compact Kähler Manifolds. A Review of ResultsMartin Schlichenmaier0Mathematics Research Unit, University of Luxembourg, FSTC, 6, rue Coudenhove-Kalergi 1359 Luxembourg-Kirchberg, LuxembourgThis article is a review on Berezin-Toeplitz operator and Berezin-Toeplitz deformation quantization for compact quantizable Kähler manifolds. The basic objects, concepts, and results are given. This concerns the correct semiclassical limit behaviour of the operator quantization, the unique Berezin-Toeplitz deformation quantization (star product), covariant and contravariant Berezin symbols, and Berezin transform. Other related objects and constructions are also discussed.http://dx.doi.org/10.1155/2010/927280
spellingShingle Martin Schlichenmaier
Berezin-Toeplitz Quantization for Compact Kähler Manifolds. A Review of Results
Advances in Mathematical Physics
title Berezin-Toeplitz Quantization for Compact Kähler Manifolds. A Review of Results
title_full Berezin-Toeplitz Quantization for Compact Kähler Manifolds. A Review of Results
title_fullStr Berezin-Toeplitz Quantization for Compact Kähler Manifolds. A Review of Results
title_full_unstemmed Berezin-Toeplitz Quantization for Compact Kähler Manifolds. A Review of Results
title_short Berezin-Toeplitz Quantization for Compact Kähler Manifolds. A Review of Results
title_sort berezin toeplitz quantization for compact kahler manifolds a review of results
url http://dx.doi.org/10.1155/2010/927280
work_keys_str_mv AT martinschlichenmaier berezintoeplitzquantizationforcompactkahlermanifoldsareviewofresults