Quantization of the sphere with coherent states
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.
Cite
@article{arxiv.math-ph/0302056,
title = {Quantization of the sphere with coherent states},
author = {Marc Lachieze Rey and Jean-Pierre Gazeau and Eric Huguet and Jacques Renaud and Tarik Garidi},
journal= {arXiv preprint arXiv:math-ph/0302056},
year = {2007}
}
Comments
9 pages, no figure. Int. J. Theor. Phys. 2003, in press