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Quantization methods: A guide for physicists and analysts. (English) Zbl 1075.81038
This paper is an excellent overview of some of the better known quantization techniques (for systems with finite numbers of degrees of freedom). A large part of this paper is devoted to geometric quantization. The other quantization techniques considered are: canonical quantization, Segal and Borel quantizations, deformation quantization (theory of star-products), Berezin and Berezin-Toeplitz quantizations, prime quantization and coherent state quantization. The authors also provide a large list of references on the subject.

MSC:
81S10 Geometry and quantization, symplectic methods
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
53D50 Geometric quantization
53D55 Deformation quantization, star products
47N50 Applications of operator theory in the physical sciences
81R30 Coherent states
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