A remark on Berezin's quantization and cut locus

Details A remark on Berezin's quantization and cut locus A remark on Berezin's quantization and cut locus

1997-07-31

arxiv.org/abs/dg-ga/9707025v1

Mathematics

Differential Geometry

8 pages, Latex2e, ams fonts, to appear in "Quantizations, Deformations and Coherent States", Edited by S. Twareque Ali, A. Odz

Scientific paper

10.1016/S0034-4877(97)85912-5

The consequences for Berezin's quantization on symmetric spaces of the identity of the set of coherent vectors orthogonal to a fixed one with the cut locus are stated precisely. It is shown that functions expressing the coherent states, the covariant symbols of operators, the diastasis function, the characteristic and two-point functions are defined when one variable does not belong to the cut locus of the other one.

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