Reference : Berezin's coherent states, symbols and transform for compact Kähler manifolds.
Parts of books : Contribution to collective works
Physical, chemical, mathematical & earth Sciences : Mathematics
Berezin's coherent states, symbols and transform for compact Kähler manifolds.
Schlichenmaier, Martin mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
Geometric Methods in Physics, XXX Workshop 2011
Trends in Mathematics
[en] Berezin-Toeplitz quantization; Kähler manifolds; geometric quantization; deformation quantization; quantum operators
[en] Coherent states are quite well known, wide-spread and extremely useful tools. In this review, coherent state techniques for general quantizable compact Kähler manifolds are reviewed. 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 setting and are uniquely defined. They are different but equivalent and the equivalence transformation is given. Results on the Berezin transform are used in an essential manner.

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