A fuzzy bipolar celestial sphere
arXiv:1901.01167 · doi:10.1007/JHEP07(2019)028
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