We briefly report on our recent construction [1] of new fuzzy spheres S^d_L of dimensions d = 1,2 covariant under the full orthogonal group O(D), D = d+1. S^d_L is built imposing a suitable energy cutoff on a quantum particle in R^D subject to a confining potential well V(r) with a very sharp minimum on the sphere of radius r =1; the cutoff and the depth of the well depend on (and diverge with) a natural number L. The commutator of the coordinates depends only on the angular momentum, as in Snyder noncommutative spaces. As L diverges, the Hilbert space dimension also diverges, S_d^L goes to the ordinary d-dimensional sphere S_d, and we recover ordinary quantum mechanics on S_d. These models might be useful in quantum field theory, quantum gravity or condensed matter physics.
New fuzzy spheres through confining potentials and energy cutoffs
Gaetano Fiore
;PISACANE, FRANCESCO
2018
Abstract
We briefly report on our recent construction [1] of new fuzzy spheres S^d_L of dimensions d = 1,2 covariant under the full orthogonal group O(D), D = d+1. S^d_L is built imposing a suitable energy cutoff on a quantum particle in R^D subject to a confining potential well V(r) with a very sharp minimum on the sphere of radius r =1; the cutoff and the depth of the well depend on (and diverge with) a natural number L. The commutator of the coordinates depends only on the angular momentum, as in Snyder noncommutative spaces. As L diverges, the Hilbert space dimension also diverges, S_d^L goes to the ordinary d-dimensional sphere S_d, and we recover ordinary quantum mechanics on S_d. These models might be useful in quantum field theory, quantum gravity or condensed matter physics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
