Quantization of Kähler manifolds. III. (English) Zbl 0826.53052

Cahen, Michel; Gutt, Simone; Rawnsley, John

Lett. Math. Phys. 30, No. 4, 291-305 (1994).

In two previous papers [J. Geom. Phys. 7, No. 1, 45-62 (1990; Zbl 0719.53044) and Trans. Am. Math. Soc. 337, No. 1, 73-98 (1993; Zbl 0788.53062)] the authors have examined various geometrical methods for the quantization of compact Kähler manifolds.
In the paper under review they make the first steps in extending these results to noncompact Kähler manifolds. As an example, the case of an open disk in \(\mathbb{C}\) with Poincaré metric is described in detail.

Reviewer: M.Puta (Timişoara)

MSC:

53C55	Global differential geometry of Hermitian and Kählerian manifolds
53D50	Geometric quantization

Keywords:

Berezin quantization; Kähler manifolds; open disk; Poincaré metric

Citations:

Zbl 0719.53044; Zbl 0788.53062

References:

[1]	Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D., Deformation theory and quantization,Lett. Math. Phys. 1, 521–530 (1977).
[2]	Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D., Deformation theory and quantization,Ann. Phys. 111, 61–110 (1978). · Zbl 0377.53024
[3]	Berezin, F. A., Quantisation of Kähler manifold,Comm. Math. Phys. 40, 153 (1975). · Zbl 1272.53082
[4]	Cahen, M., Gutt, S., and Rawnsley, J., Quantization of Kähler manifolds I: geometric interpretation of Berezin’s quantisation,J. Geom. Phys. 7, 45–62 (1990). · Zbl 0736.53056
[5]	Cahen, M., Gutt, S., and Rawnsley, J., Quantization of Kähler manifolds. II,Trans. Amer. Math. Soc. 337, 73–98 (1993). · Zbl 0788.53062
[6]	Combet, E.,Intégrales exponentielles., Lecture Notes in Mathematics 937, Springer-Verlag, Berlin, Heidelberg, New York, 1982. · Zbl 0509.58019
[7]	Moreno, C.,* products onD 1(\(\mathbb{C}\),S 2) and related spectral analysis,Lett. Math. Phys. 7, 181–193 (1983). · Zbl 0528.58014