Abstract
We study the eigenvalue equation for the ‘Cartesian coordinates’ observables xi on the fully -covariant fuzzy circle () and on the fully -covariant fuzzy 2-sphere () introduced in (Fiore and Pisacane 2018 J. Geom. Phys. 132 423–51). We show that the spectrum and eigenvectors of xi fulfill a number of properties which are expected for xi to approximate well the corresponding coordinate operator of a quantum particle forced to stay on the unit sphere.
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