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 |
| Creators: | Creators Email Pisacane, Francesco francesco.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: | nome email de Giovanni, Francesco francesco.degiovanni2@unina.it |
| Tutor: | nome email Fiore, Gaetano UNSPECIFIED |
| 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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