New fuzzy spheres through confining potentials and energy cutoffs
Abstract
We briefly report our recent construction of new fuzzy spheres of dimensions d=1,2 covariant under the full orthogonal group O(D), D=d+1. They are built by imposing a suitable energy cutoff on a quantum particle in D dimensions subject to a confining potential well V(r) with a very sharp minimum on the sphere of radius r=1; furthermore, 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. When L diverges, the Hilbert space dimension diverges, too; S^d_L converges to 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.
Keywords
Cite
@article{arxiv.1807.09053,
title = {New fuzzy spheres through confining potentials and energy cutoffs},
author = {Gaetano Fiore and Francesco Pisacane},
journal= {arXiv preprint arXiv:1807.09053},
year = {2019}
}
Comments
Latex file, 13 pages, 2 figures. Contribution to the proceedings of the Corfu Summer Institute "School and Workshops on Elementary Particle Physics and Gravity", 2-28 September 2017, Corfu, Greece. Version 3: some misprints in the published version are corrected