dorsal/arxiv
View SchemaThe q-Euclidean algebra $U_q(e^N)$ and the corresponding q-Euclidean lattice
| Authors | Gaetano Fiore |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9506028 |
| URL | https://arxiv.org/abs/q-alg/9506028 |
| DOI | 10.1142/S0217751X96000390 |
| Journal | Int. J. Mod. Phys. A11 (1996), 863-886 |
Abstract
We review the Euclidean Hopf algebra $U_q(e^N)$ dual of $Fun(\rn_q^N\lcross SO_{q^{-1}}(N))$ and describe its fundamental Hilbert space representations \cite{fioeu}, which turn out to be rather simple "lattice-regularized" versions of the classical ones, in the sense that the spectra of squared momentum components are discrete and the corresponding eigenfunctions normalizable.These representations can be regarded as describing a quantum system consisting of one free particle on the quantum Euclidean space. A suitable notion of classical limit is introduced, so that we recover the classical continuous spectra and generalized (non-normalizable) eigenfunctions in that limit.
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"abstract": "We review the Euclidean Hopf algebra $U_q(e^N)$ dual of $Fun(\\rn_q^N\\lcross\nSO_{q^{-1}}(N))$ and describe its fundamental Hilbert space representations\n\\cite{fioeu}, which turn out to be rather simple \"lattice-regularized\" versions\nof the classical ones, in the sense that the spectra of squared momentum\ncomponents are discrete and the corresponding eigenfunctions normalizable.These\nrepresentations can be regarded as describing a quantum system consisting of\none free particle on the quantum Euclidean space. A suitable notion of\nclassical limit is introduced, so that we recover the classical continuous\nspectra and generalized (non-normalizable) eigenfunctions in that limit.",
"arxiv_id": "q-alg/9506028",
"authors": [
"Gaetano Fiore"
],
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"q-alg",
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],
"doi": "10.1142/S0217751X96000390",
"journal_ref": "Int. J. Mod. Phys. A11 (1996), 863-886",
"title": "The q-Euclidean algebra $U_q(e^N)$ and the corresponding q-Euclidean lattice",
"url": "https://arxiv.org/abs/q-alg/9506028"
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