Berezin-toeplitz Quantization and Berezin Symbols for Arbitrary Compact K ¨ Ahler Manifolds

  title={Berezin-toeplitz Quantization and Berezin Symbols for Arbitrary Compact K ¨ Ahler Manifolds},
  author={Martin Schlichenmaier and E. Meinrenken and M. Schlichenmaier and S. Klimek and A. Lesniewski}
For phase-space manifolds which are compact Kähler manifolds relations between the Berezin-Toeplitz quantization and the quantization using Berezin's coherent states and symbols are studied. First, results on the Berezin-Toeplitz quanti-zation of arbitrary quantizable compact Kähler 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 Kähler manifolds is discussed. 1… CONTINUE READING
Highly Cited
This paper has 17 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.
12 Citations
11 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 11 references

Coherent states and Kähler manifolds

  • J. H. Rawnsley
  • Mathematical Topics between Classical and Quantum…
  • 1998

On the correspondence principle for the quantized annulus

  • A. Lesniewski Klimek
  • Math . Scand .
  • 1996

The Berezin transform and invariant differential operators

  • H. Upmeier Unterberger
  • Zwei Anwendungen algebraisch…
  • 1996

Asymptotics of the Berezin transform and quantization on planar domains

  • Englǐs
  • Duke Math . J .
  • 1995

Quantization of Kähler manifolds II

  • Englǐs
  • Trans . Amer . Math . Soc .
  • 1993

gl ( ∞ ) and geometric quantization

  • E. Meinrenken Bordemann, M. Schlichenmaier
  • Commun . Math . Phys .
  • 1991

Quantization of Kähler manifolds I : Geometric interpretation of Berezin ’ s quantization

  • S. Gutt, J. Rawnsley
  • JGP
  • 1990

Similar Papers

Loading similar papers…