Quantization of the sphere with coherent states

2003/02/24 by Marc Lachieze Rey, Jean-Pierre Gazeau, Rey, Marc Lachieze +7
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.MP #math.OA

paper · pdf · doi:10.48550/arxiv.math-ph/0302056

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

arxiv created 2003/02/24 · arxiv updated 2009/11/30

Abstract

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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