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Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis (CROSBI ID 264398)

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Jurman, Danijel Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis // Fortschritte der Physik = Progress of physics, 67 (2019), 4; 1800061, 8. doi: 10.1002/prop.201800061

Podaci o odgovornosti

Jurman, Danijel

engleski

Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis

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.

fuzzy/non‐commutative de Sitter space ; kappa‐Minkowski space ; matrix geometry

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Podaci o izdanju

67 (4)

2019.

1800061

8

objavljeno

0015-8208

1521-3978

10.1002/prop.201800061

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Fizika

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