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

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

2010-03-12

arxiv.org/abs/1003.2523v1

Mathematics

Quantum Algebra

32 pages

Scientific paper

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.

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