Abstract
For arbitrary compact quantizable Kahler 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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Schlichenmaier, M. (2000). Deformation quantization of compact Kähler manifolds by Berezin-Toeplitz quantization. In: Dito, G., Sternheimer, D. (eds) Conférence Moshé Flato 1999. Mathematical Physics Studies, vol 21/22. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1276-3_22
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DOI: https://doi.org/10.1007/978-94-015-1276-3_22
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