The Fuzzy Sphere: From The Uncertainty Relation To The Stereographic Projection
Musongela Lubo
Abstract
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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