HAL : hal-00122710, version 1

arXiv : math-ph/0302056

Code Bibliographique ADS : 2003math.ph...2056L

DOI : 10.1023/A:1025762717014

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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 - AstroParticule et Cosmologie

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:

Mathématiques/Physique mathématique Physique/Physique mathématique Mathématiques/Algèbres d'opérateurs

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Soumis le : Jeudi 4 Janvier 2007, 14:29:23

Dernière modification le : Vendredi 24 Février 2012, 13:49:42