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Article Dans Une Revue International Journal of Theoretical Physics Année : 2003

Quantization of the sphere with coherent states

J.-P. Gazeau

Résumé

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.

Dates et versions

hal-00122710 , version 1 (04-01-2007)

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Citer

M. Lachièze-Rey, J.-P. Gazeau, E. Huguet, J. Renaud, T. Garidi. Quantization of the sphere with coherent states. International Journal of Theoretical Physics, 2003, 42, pp.1301-1310. ⟨10.1023/A:1025762717014⟩. ⟨hal-00122710⟩
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