Fuzzy spheres from inequivalent coherent states quantizations

J.-P. Gazeau , E. Huguet , M. Lachièze-Rey , J. Renaud

The existence of a family of coherent states (CS) solving the identity in a Hilbert space allows, under certain conditions, to quantize functions defined on the measure space of CS parameters. The application of this procedure to the 2-sphere provides a family of inequivalent CS quantizations based on the spin spherical harmonics (the CS quantization from usual spherical harmonics appears to give a trivial issue for the Cartesian coordinates). We compare these CS quantizations to the usual (Madore) construction of the fuzzy sphere. Due to these differences, our procedure yields new types of fuzzy spheres. Moreover, the general applicability of CS quantization suggests similar constructions of fuzzy versions of a large variety of sets.

Mots clés: fuzzy sphere; coherent states; spin spherical harmonics; Quantization

Domaines: Physique Quantique [quant-ph]

J.-P. Gazeau, E. Huguet, M. Lachièze-Rey, J. Renaud. Fuzzy spheres from inequivalent coherent states quantizations. Journal of Physics A: Mathematical and Theoretical, 2007, 40, pp.10225-10249. ⟨10.1088/1751-8113/40/33/018⟩. ⟨hal-00105288⟩