New fuzzy spheres through confining potentials and energy cutoffs
August 22, 2018
August 24, 2018
We briefly report on our recent construction  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 diverges as well, S^d_L goes 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.
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