Deformation quantization of compact Kaehler manifolds by Berezin-Toeplitz quantization

Details Deformation quantization of compact Kaehler manifolds by Berezin-Toeplitz quantization Deformation quantization of compact Kaehler manifolds by Berezin-Toeplitz quantization

1999-10-26

arxiv.org/abs/math/9910137v1

Mathematics

Quantum Algebra

Amslatex, 18 pages

Scientific paper

For arbitrary compact quantizable Kaehler manifolds it is shown how a natural formal deformation quantization (star product) can be obtained via Berezin-Toeplitz operators. Results on their semi-classical behaviour (their asymptotic expansion) due to Bordemann, Meinrenken and Schlichenmaier are used in an essential manner. It is shown that the star product is null on constants and fulfills parity. A trace is constructed and the relation to deformation quantization by geometric quantization is given.

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