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- W3052473179 abstract "Projecting a quantum theory onto the Hilbert subspace of states with energies below a cutoff $overline{E}$ may lead to an effective theory with modified observables, including a noncommutative space(time). Adding a confining potential well $V$ with a very sharp minimum on a submanifold $N$ of the original space(time) $M$ may induce a dimensional reduction to a noncommutative quantum theory on $N$. Here in particular we briefly report on our application of this procedure to spheres $S^dsubsetmathbb{R}^D$ of radius $r=1$ ($D=d!+!1>1$): making $overline{E}$ and the depth of the well depend on (and diverge with) $Lambdainmathbb{N}$ we obtain new fuzzy spheres $S^d_{Lambda}$ covariant under the {it full} orthogonal groups $O(D)$; the commutators of the coordinates depend only on the angular momentum, as in Snyder noncommutative spaces. Focusing on $d=1,2$, we also discuss uncertainty relations, localization of states, diagonalization of the space coordinates and construction of coherent states. As $Lambdatoinfty$ the Hilbert space dimension diverges, $S^d_{Lambda}to S^d$, and we recover ordinary quantum mechanics on $S^d$. These models might be suggestive for effective models in quantum field theory, quantum gravity or condensed matter physics." @default.
- W3052473179 created "2020-08-24" @default.
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- W3052473179 date "2020-08-18" @default.
- W3052473179 modified "2023-09-27" @default.
- W3052473179 title "Energy cutoff, effective theories, noncommutativity, fuzzyness: the case of $O(D)$-covariant fuzzy spheres" @default.
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- W3052473179 doi "https://doi.org/10.22323/1.376.0208" @default.
- W3052473179 hasPublicationYear "2020" @default.
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