Identification of Berezin-Toeplitz deformation quantization

Details Identification of Berezin-Toeplitz deformation quantization Identification of Berezin-Toeplitz deformation quantization

2000-06-08

arxiv.org/abs/math/0006063v1

Mathematics

Quantum Algebra

26 pages

Scientific paper

We give a complete identification of the deformation quantization which was obtained from the Berezin-Toeplitz quantization on an arbitrary compact Kaehler manifold. The deformation quantization with the opposite star-product proves to be a differential deformation quantization with separation of variables whose classifying form is explicitly calculated. Its characteristic class (which classifies star-products up to equivalence) is obtained. The proof is based on the microlocal description of the Szegoe kernel of a strictly pseudoconvex domain given by Boutet de Monvel and Sjoestrand.

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