We study the eigenvalue equation for the "Cartesian coordinates" observables x_i (i=1,2) on the fully O(2)-covariant fuzzy circle S^1_L and x_i (i=1,2,3) on the fully O(3)-covariant fuzzy 2-sphere S^2_L introduced in [G. Fiore, F. Pisacane, J. Geom. Phys. 132 (2018), 423-451]. We show that the spectrum and eigenvectors of x_i ful fill a number of properties which are expected for x_i to approximate well the corresponding coordinate operator of a quantum particle forced to stay on the unit sphere.
The x_i-eigenvalue problem on some new fuzzy spheres / Fiore, Gaetano; Pisacane, Francesco. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 53:9(2020), p. 095201. [10.1088/1751-8121/ab67e3]
The x_i-eigenvalue problem on some new fuzzy spheres
Fiore, Gaetano;Pisacane, Francesco
2020
Abstract
We study the eigenvalue equation for the "Cartesian coordinates" observables x_i (i=1,2) on the fully O(2)-covariant fuzzy circle S^1_L and x_i (i=1,2,3) on the fully O(3)-covariant fuzzy 2-sphere S^2_L introduced in [G. Fiore, F. Pisacane, J. Geom. Phys. 132 (2018), 423-451]. We show that the spectrum and eigenvectors of x_i ful fill a number of properties which are expected for x_i to approximate well the corresponding coordinate operator of a quantum particle forced to stay on the unit sphere.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
