Berezin-Toeplitz quantization for compact Kaehler manifolds. A Review of Results

Abstract

This article is a review on Berezin-Toeplitz operator and Berezin-Toeplitz deformation quantization for compact quantizable Kaehler manifolds. The basic objects, concepts, and results are given. This concerns the correct semi-classical 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.

32 pages

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• The classical limit of mean-field quantum spin systems
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• Quantum Logic and Geometric quantization
• Semi-Classical Limit of Quantum Gravity on Corners
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