Pisacane, Francesco
(2019)
The O(D)-equivariant fuzzy hyperspheres.
[Tesi di dottorato]
Tipologia del documento: |
Tesi di dottorato
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Lingua: |
English |
Titolo: |
The O(D)-equivariant fuzzy hyperspheres |
Autori: |
Autore | Email |
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Pisacane, Francesco | francesco.pisacane@unina.it |
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Data: |
11 Dicembre 2019 |
Numero di pagine: |
196 |
Istituzione: |
Università degli Studi di Napoli Federico II |
Dipartimento: |
Matematica e Applicazioni "Renato Caccioppoli" |
Dottorato: |
Scienze matematiche e informatiche |
Ciclo di dottorato: |
32 |
Coordinatore del Corso di dottorato: |
nome | email |
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de Giovanni, Francesco | francesco.degiovanni2@unina.it |
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Tutor: |
nome | email |
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Fiore, Gaetano | [non definito] |
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Data: |
11 Dicembre 2019 |
Numero di pagine: |
196 |
Parole chiave: |
Geometria non commutativa, fuzzy spaces |
Settori scientifico-disciplinari del MIUR: |
Area 01 - Scienze matematiche e informatiche > MAT/07 - Fisica matematica |
[error in script]
[error in script]
Depositato il: |
13 Gen 2020 13:05 |
Ultima modifica: |
17 Nov 2021 12:10 |
URI: |
http://www.fedoa.unina.it/id/eprint/12965 |
Abstract
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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