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International Journal of Theoretical Physics 42 (2003) 1301-1310
Quantization of the sphere with coherent states
M. Lachièze-Rey1, J.-P. Gazeau1, E. Huguet1, J. Renaud1, T. Garidi1
(2003)

Quantization with coherent states allows to " quantize " any space X of parameters. In the case where X is a phase space, this leads to the usual quantum mechanics. But the procedure is much more general, and does not require a symplectic, or any kind of structure in X, other than a measure. It is simply considered as a different way to look at the system, the choice of a resolution, in analogy with data handling, where coherent states (e.g., under the form of wavelets) are very efficient. Here, we present the complex coherent states quantization of the 2-sphere, with emphasis on the links with group representation. We show how this procedure leads naturally to the fuzzy sphere and to non commutative geometry.
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
Mathématiques/Physique mathématique

Physique/Physique mathématique

Mathématiques/Algèbres d'opérateurs
Lien vers le texte intégral : 
http://fr.arXiv.org/abs/math-ph/0302056