Pisacane, Francesco (2019) The O(D)-equivariant fuzzy hyperspheres. [Tesi di dottorato]


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Item Type: Tesi di dottorato
Resource language: English
Title: The O(D)-equivariant fuzzy hyperspheres
Pisacane, Francescofrancesco.pisacane@unina.it
Date: 11 December 2019
Number of Pages: 196
Institution: Università degli Studi di Napoli Federico II
Department: Matematica e Applicazioni "Renato Caccioppoli"
Dottorato: Scienze matematiche e informatiche
Ciclo di dottorato: 32
Coordinatore del Corso di dottorato:
de Giovanni, Francescofrancesco.degiovanni2@unina.it
Date: 11 December 2019
Number of Pages: 196
Keywords: Geometria non commutativa, fuzzy spaces
Settori scientifico-disciplinari del MIUR: Area 01 - Scienze matematiche e informatiche > MAT/07 - Fisica matematica
Date Deposited: 13 Jan 2020 13:05
Last Modified: 17 Nov 2021 12:10
URI: http://www.fedoa.unina.it/id/eprint/12965

Collection description

We present some new fuzzy spheres of dimensions d≥1 covariant under the full orthogonal group O(D), D=d+1. They are built by imposing a sufficiently low energy cutoff on a quantum particle in the D-dimensional real euclidean space, subject to a confining potential well V(r) having a very sharp minimum on the sphere of radius r=1; furthermore, as the cutoff and the depth of the well depend on (and diverge with) a natural number Ʌ, so do the Hilbert space and the algebra of observables, ensuring that the latter actually characterize a fuzzy space. The commutator of the coordinates depends only on the angular momentum, as in it Snyder noncommutative spaces; and as Ʌ→+∞ the Hilbert space dimension diverges, the fuzzy d-dimensional hypersphere converges to the usual d-dimensional hypersphere, so we recover ordinary quantum mechanics on it. In addition, we study the eigenvalue equation for the "cartesian coordinates" observables on the fuzzy d-dimensional hypersphere and then we construct various systems of coherent states (SCS) on the fuzzy circle (d=1) and the fuzzy sphere (d=2). These models might be useful in quantum field theory, quantum gravity or condensed matter physics.


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