Jurman, Danijel (2019) Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis. Fortschritte der Physik, 67 (4). pp. 1-8. ISSN 0015-8208
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Abstract
We consider the Lie group generated by the Lie algebra of kappa-Minkowski space. Imposing the invariance of the metric under the pull-back of diffeomorphisms induced by right translations in the group, we show that a unique right invariant metric is associated with this group. This metric coincides with the metric of de Sitter space-time. We analyze the structure of unitary representations of the group which are relevant for the realization of the non-commutative κ- Minkowski space by embedding into (2D−1)- dimensional Heisenberg algebra. Using a suitable set of generalized coherent states, we select the particular Hilbert space and realize the non-commutative kappa-Minkowski space as an algebra of the Hilbert-Schmidt operators. We define dequantization map and fuzzy variant of the Laplace-Beltrami operator such that dequantization map relates fuzzy eigenvectors with the eigenfunctions of the Laplace-Beltrami operator on the half of de Sitter space-time.
| Item Type: | Article | ||||||||||||
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| Uncontrolled Keywords: | fuzzy/non‐commutative de Sitter space ; kappa‐Minkowski space ; matrix geometry | ||||||||||||
| Subjects: | NATURAL SCIENCES > Mathematics > Geometry and Topology NATURAL SCIENCES > Physics > General and Classical Physics NATURAL SCIENCES > Physics > Physics of Elementary Particles and Fields |
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| Divisions: | Theoretical Physics Division | ||||||||||||
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| Depositing User: | Danijel Jurman | ||||||||||||
| Date Deposited: | 14 Dec 2020 09:53 | ||||||||||||
| URI: | http://fulir.irb.hr/id/eprint/6125 | ||||||||||||
| DOI: | 10.1002/prop.201800061 |
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