Quantization of Kähler manifolds. IV. (English) Zbl 0831.58026

Cahen, Michel; Gutt, Simone; Rawnsley, John

Lett. Math. Phys. 34, No. 2, 159-168 (1995).

Summary: We use Berezin’s dequantization procedure to define a formal \(*\)-product on the algebra of smooth functions on the bounded symmetric domains. We prove that this formal \(*\)-product is convergent on a dense subalgebra of the algebra of smooth functions.
[For part I–III see the authors, J. Geom. Phys. 7, No. 1, 45-62 (1990; Zbl 0719.53044), Trans. Am. Math. Soc. 337, No. 1, 73-98 (1993; Zbl 0788.53062), and Lett. Math. Phys. 30, No. 4, 291-305 (1994; Zbl 0826.53052), respectively].

MSC:

53D50	Geometric quantization
32M15	Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)

Keywords:

polynomial differential operators; Berezin’s dequantization; bounded symmetric domains

Citations:

Zbl 0826.53052; Zbl 0719.53044; Zbl 0788.53062

References:

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