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Berezin’s Coherent States, Symbols and Transform for Compact Kähler Manifolds

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Book cover Geometric Methods in Physics

Part of the book series: Trends in Mathematics ((TM))

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Abstract

We review coherent state techniques for general quantizable compact Kähler manifolds. Discussed are co- and contravariant Berezin symbols, Berezin-Toeplitz quantization, the Berezin transform, and related natural deformation quantizations (star products). These are the Berezin-Toeplitz, the Berezin, and the Geometric Quantization star product. All three star products exist in this settinga nd are uniquely defined. They are different, but equivalent. The equivalence transformation is given. Results on the Berezin transform are used in an essential manner.

Mathematics Subject Classification (2010). Primary 53D55; Secondary 32J27, 47B35, 53D50.

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Authors and Affiliations

  1. Mathematics Research Unit, FSTC, University of Luxembourg, Campus Kirchberg, 6, rue Coudenhove-Kalergi, L-1359, Luxembourg-Kirchberg, Luxembourg

    Martin Schlichenmaier

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  1. Martin Schlichenmaier
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Correspondence to Martin Schlichenmaier .

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Editors and Affiliations

  1. Departamento de Física, CINVESTAV, Mexico City, Distrito Federal, Mexico

    Piotr Kielanowski

  2. Dept. of Mathematics and Statistics, Concordia University, Montreal, Québec, Canada

    S. Twareque Ali

  3. Institute of Mathematics, University of Bialystok, Bialystok, Poland

    Anatol Odzijewicz

  4. Mathematics Research Unit, FSTC, University of Luxembourg, Luxembourg-Kirchberg, Luxembourg

    Martin Schlichenmaier

  5. School of Mathematics, University of Manchester, Manchester, United Kingdom

    Theodore Voronov

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Schlichenmaier, M. (2013). Berezin’s Coherent States, Symbols and Transform for Compact Kähler Manifolds. In: Kielanowski, P., Ali, S., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0448-6_9

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