A fuzzy bipolar celestial sphere

Abstract

We introduce a non-commutative deformation of the algebra of bipolar spherical harmonics supporting the action of the full Lorentz algebra. Our construction is close in spirit to the one of the non-commutative spherical harmonics associated to the fuzzy sphere and, as such, it leads to a maximal value of the angular momentum. We derive the action of Lorentz boost generators on such non-commutative spherical harmonics and show that it is compatible with the existence of a maximal angular momentum.

15 pages, 4 figures; v2: typos corrected, references added; v3 title slightly changed, minor adjustments in the presentation, results unchanged. References added, matches published version

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Cited by in corpus (3)

• BMS algebras in 4 and 3 dimensions, their quantum deformations and duals
• The $x_i$-eigenvalue problem on some new fuzzy spheres
• Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains