Quantization of the sphere with coherent states

Details Quantization of the sphere with coherent states Quantization of the sphere with coherent states

2003-02-24

arxiv.org/abs/math-ph/0302056v1

Physics

Mathematical Physics

9 pages, no figure. Int. J. Theor. Phys. 2003, in press

Scientific paper

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.

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