dorsal/arxiv
View SchemaQuantum Orthogonal Planes: ISO_{q,r}(N) and SO_{q,r}(N) -- Bicovariant Calculi and Differential Geometry on Quantum Minkowski Space
| Authors | Paolo Aschieri, Leonardo Castellani, Antonio Maria Scarfone |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9709032 |
| URL | https://arxiv.org/abs/q-alg/9709032 |
| DOI | 10.1007/s100529800968 |
| Journal | Eur.Phys.J.C7:159-175,1999 |
Abstract
We construct differential calculi on multiparametric quantum orthogonal planes in any dimension N. These calculi are bicovariant under the action of the full inhomogeneous (multiparametric) quantum group ISO_{q,r}(N), and do contain dilatations. If we require bicovariance only under the quantum orthogonal group SO_{q,r}(N), the calculus on the q-plane can be expressed in terms of its coordinates x^a, differentials dx^a and partial derivatives \partial_a without the need of dilatations, thus generalizing known results to the multiparametric case. Using real forms that lead to the signature (n+1,m) with m = n-1, n, n+1 , we find ISO_{q,r}(n+1, m) and SO_{q,r}(n+1,m) bicovariant calculi on the multiparametric quantum spaces. The particular case of the quantum Minkowski space ISO_{q,r}(3,1)/SO_{q,r}(3,1) is treated in detail. The conjugated partial derivatives \partial_a* can be expressed as linear combinations of the \partial_a. This allows a deformation of the phase-space where no additional operators (besides x^a and p_a) are needed.
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"abstract": "We construct differential calculi on multiparametric quantum orthogonal\nplanes in any dimension N. These calculi are bicovariant under the action of\nthe full inhomogeneous (multiparametric) quantum group ISO_{q,r}(N), and do\ncontain dilatations.\n If we require bicovariance only under the quantum orthogonal group\nSO_{q,r}(N), the calculus on the q-plane can be expressed in terms of its\ncoordinates x^a, differentials dx^a and partial derivatives \\partial_a without\nthe need of dilatations, thus generalizing known results to the multiparametric\ncase. Using real forms that lead to the signature (n+1,m) with m = n-1, n, n+1\n, we find ISO_{q,r}(n+1, m) and SO_{q,r}(n+1,m) bicovariant calculi on the\nmultiparametric quantum spaces. The particular case of the quantum Minkowski\nspace ISO_{q,r}(3,1)/SO_{q,r}(3,1) is treated in detail.\n The conjugated partial derivatives \\partial_a* can be expressed as linear\ncombinations of the \\partial_a. This allows a deformation of the phase-space\nwhere no additional operators (besides x^a and p_a) are needed.",
"arxiv_id": "q-alg/9709032",
"authors": [
"Paolo Aschieri",
"Leonardo Castellani",
"Antonio Maria Scarfone"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"doi": "10.1007/s100529800968",
"journal_ref": "Eur.Phys.J.C7:159-175,1999",
"title": "Quantum Orthogonal Planes: ISO_{q,r}(N) and SO_{q,r}(N) -- Bicovariant Calculi and Differential Geometry on Quantum Minkowski Space",
"url": "https://arxiv.org/abs/q-alg/9709032"
},
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