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**Quantization on curved manifolds.**
*(English)*
Zbl 1009.53061

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 3rd international conference on geometry, integrability and quantization, Varna, Bulgaria, June 14-23, 2001. Sofia: Coral Press Scientific Publishing. 64-104 (2002).

Since the early days of quantum mechanics, several methods have been developed in order to deal with manifolds supporting non-trivial topology. Among them, two techniques have received a great attention because they are most geometrical in nature. These are the Kostant-Souriau geometric quantization scheme and the so-called constrained quantum mechanics. The present paper is an excellent survey of these two methods and both approaches are illustrated in full detail. The presented examples include the \(n\)-dimensional oscillator and the Kepler problem which are treated within geometric quantization scheme using the well-known Marsden-Weinstein reduction and even a combination of both methods is applied in the study of geodesic flow on axisymmetric ellipsoids.

For the entire collection see [Zbl 0980.00035].

For the entire collection see [Zbl 0980.00035].

Reviewer: Mircea Crâşmăreanu (Iaşi)