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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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2010/927280 |
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| _version_ | 1849305157425168384 |
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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. |
| format | Article |
| id | doaj-art-0376c8e4cd834e589ced58f4475125d2 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| 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 |