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- W3004426347 abstract "Fuzzy hyperspheres $S^d_Lambda$ of dimension $d>2$ are constructed here generalizing the procedure adopted in [G. Fiore, F. Pisacane, J. Geom. Phys. 132 (2018), 423-451] for $d=1,2$. The starting point is an ordinary quantum particle in $mathbb{R}^D$, $D:=d+1$, subject to a rotation invariant potential well $V(r)$ with a very sharp minimum on the sphere of radius $r=1$. The subsequent imposition of a sufficiently low energy cutoff `freezes' the radial excitations, this makes only a finite-dimensional Hilbert subspace $mathcal{H}_{Lambda,D}$ accessible and on it the coordinates noncommutative {it a la Snyder}. In addition, the coordinate operators generate the whole algebra of observables $mathcal{A}_{Lambda,D}$ which turns out to be realizable through a suitable irreducible vector representation of $Uso(D+1)$. This construction is equivariant not only under $SO(D)$, but under the full orthogonal group $O(D)$, and making the cutoff and the depth of the well grow with a natural number $Lambda$, the result is a sequence $S^d_{Lambda}$ of fuzzy spheres converging to $S^d$ as $Lambdatoinfty$ (where one recovers ordinary quantum mechanics on $S^d$)." @default.
- W3004426347 created "2020-02-14" @default.
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- W3004426347 date "2020-02-05" @default.
- W3004426347 modified "2023-09-27" @default.
- W3004426347 title "$O(D)-$equivariant fuzzy hyperspheres" @default.
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