The Fuzzy Sphere: From The Uncertainty Relation To The Stereographic Projection

Details The Fuzzy Sphere: From The Uncertainty Relation To The Stereographic Projection The Fuzzy Sphere: From The Uncertainty Relation To The Stereographic Projection

2004-03-22

arxiv.org/abs/hep-th/0403214v2

JHEP 0405 (2004) 052

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, Latex. Minor changes in notations. Version to appear in JHEP

Scientific paper

10.1088/1126-6708/2004/05/052

On the fuzzy sphere, no state saturates simultaneously all the Heisenberg uncertainties. We propose a weaker uncertainty for which this holds. The family of states so obtained is physically motivated because it encodes information about positions in this fuzzy context. In particular, these states realize in a natural way a deformation of the stereographic projection. Surprisingly, in the large $j$ limit, they reproduce some properties of the ordinary coherent states on the non commutative plane.

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