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 / Fiore, Gaetano; Pisacane, Francesco. - In: POS PROCEEDINGS OF SCIENCE. - ISSN 1824-8039. - 318:(2018). (Intervento presentato al convegno Workshop on Testing Fundamental Physics Principles tenutosi a Mon-Repos, Corfu, Greece nel 22-28nsettembre 2017) [10.22323/1.318.0184].

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.
2018
New fuzzy spheres through confining potentials and energy cutoffs / Fiore, Gaetano; Pisacane, Francesco. - In: POS PROCEEDINGS OF SCIENCE. - ISSN 1824-8039. - 318:(2018). (Intervento presentato al convegno Workshop on Testing Fundamental Physics Principles tenutosi a Mon-Repos, Corfu, Greece nel 22-28nsettembre 2017) [10.22323/1.318.0184].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/721323
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