Berezin-Toeplitz quantization and Berezin symbols for arbitrary compact Kaehler manifolds

Details Berezin-Toeplitz quantization and Berezin symbols for arbitrary compact Kaehler manifolds Berezin-Toeplitz quantization and Berezin symbols for arbitrary compact Kaehler manifolds

1999-02-10

arxiv.org/abs/math/9902066v2

Mathematics

Quantum Algebra

11 pages, Amslatex, some annoying typos removed (missing superscript, or superscripts at the wrong places)

Scientific paper

For phase-space manifolds which are compact Kaehler manifolds relations between the Berezin-Toeplitz quantization and the quantization with the help of Berezin's coherent states and symbols are studied. First the results on the Berezin-Toeplitz quantization of arbitrary compact Kaehler manifolds due to Bordemann, Meinrenken and Schlichenmaier are recalled. It is shown that the covariant symbol map is adjoint to the Toeplitz map. The Berezin transform for compact Kaehler manifolds is discussed. (Talk presented at the XVII workshop on geometric methods in physics, Bialowieza, Poland, July 3 --July 9, 1998)

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