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Quantization of Kaehler manifolds. I: Geometric interpretation of Berezin's quantization

Authors
  • Rawnsley, J.
  • Cahen, M.
  • Gutt, S.
Publication Date
Jan 01, 1990
Identifiers
DOI: 10.1016/0393-0440(90)90019-Y
OAI: oai:inspirehep.net:306668
Source
INSPIRE-HEP
Keywords
License
Unknown
External links

Abstract

We give a geometric interpretation of Berezin's symbolic calculus on Kähler manifolds in the framework of geometric quantization. Berezin's covariant symbols are defined in terms of coherent states and we study a function ϴ on the manifold which is the central object of the theory. When this function is constant Berezin's quantization rule coincides with the prescription of geometric quantization for the quantizable functions. It is defined on a larger class of functions. We show in the compact homogeneous case how to extend Berezin's procedure to a dense subspace of the algebra of smooth functions.

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