The κ-(A)dS noncommutative spacetime

The (3+1)-dimensional κ-(A)dS noncommutative spacetime is explicitly constructed by quantizing its semiclassical counterpart, which is the κ-(A)dS Poisson homogeneous space. This turns out to be the only possible generalization of the well-known κ-Minkowski spacetime to the case of non-vanishing cos...

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Bibliographic Details
Published in:Physics letters. B 2019-09, Vol.796, p.93-101
Main Authors: Ballesteros, Angel, Gutierrez-Sagredo, Ivan, Herranz, Francisco J.
Format: Article
Language:English
Subjects:
(Anti-)de Sitter
Cosmological constant
Kappa-deformation
Noncommutative spacetimes
Quantization
Quantum groups
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Summary:The (3+1)-dimensional κ-(A)dS noncommutative spacetime is explicitly constructed by quantizing its semiclassical counterpart, which is the κ-(A)dS Poisson homogeneous space. This turns out to be the only possible generalization of the well-known κ-Minkowski spacetime to the case of non-vanishing cosmological constant, under the condition that the time translation generator of the corresponding quantum (A)dS algebra is primitive. Moreover, the κ-(A)dS noncommutative spacetime is shown to have a quadratic subalgebra of local spatial coordinates whose first-order brackets in terms of the cosmological constant parameter define a quantum sphere, while the commutators between time and space coordinates preserve the same structure of the κ-Minkowski spacetime. When expressed in ambient coordinates, the quantum κ-(A)dS spacetime is shown to be defined as a noncommutative pseudosphere.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2019.07.038