Proceedings of Corfu Summer Institute 2022 "School and Workshops on Elementary Particle Physics and Gravity" β€” PoS(CORFU2022) 2023
DOI: 10.22323/1.436.0344
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General O(D)-equivariant fuzzy hyperspheres via confining potentials and energy cutoffs

Gaetano Fiore

Abstract: We summarize our recent construction [1-3] of new fuzzy hyperspheres 𝑆 𝑑 Ξ› of arbitrary dimension 𝑑 ∈ N covariant under the full orthogonal group 𝑂 (𝐷), 𝐷 = 𝑑 +1. We impose a suitable energy cutoff on a quantum particle in R 𝐷 subject to a confining potential well 𝑉 (π‘Ÿ) with a very sharp minimum on the sphere of radius π‘Ÿ = 1; the cutoff and the depth of the well diverge with Ξ› ∈ N. Consequently, the commutators of the Cartesian coordinates π‘₯ 𝑖 are proportional to the angular momentum components 𝐿… Show more

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