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Quantization of Kähler manifolds I: geometric interpretation of Berezin's quantization
Abstract We give a geometric interpretation of Berezin's symbolic calculus on Kahler manifolds in the framework of geometric quantization. Berezin's covariant symbols are defined in terms of coherentExpand
Quantization of Kähler manifolds II
We use Berezin’s dequantization procedure to define a formal *- product on a dense subalgebra of the algebra ofsmooth functions on a compact homogeneous Kahler manifold M. We prove that this formalExpand
Quantization of Kähler manifolds. III
We use Berezin's dequantization procedure to define a formal *-product on the algebra of smooth functions on the unit disk in ℂ. We prove that this formal *-product is convergent on a denseExpand
Equivalence of star products on a symplectic manifold
Abstract These notes grew out of the Quantisation Seminar 1997–1998 on Deligne's paper [P. Deligne, Deformations de l'algebre des fonctions d'une variete symplectique: Comparison entre Fedosov et DeExpand
Representations of a semi-direct product by quantization
1. Introduction . The purpose of this note is to apply the Kostant-Souriau quantization theory (2, 3, 4, 5, 7) to construct representations of a semi-direct product.
Symplectic connections
This article is an overview of the results obtained in recent years on symplectic connections. We present what is known about preferred connections (critical points of a variational principle). TheExpand