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arXiv · 1711.05050

Curved momentum spaces from quantum (Anti-)de Sitter groups in (3+1) dimensions

Angel Ballesteros·Giulia Gubitosi·Iván Gutiérrez-Sagredo·Francisco J. Herranz
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Abstract

Curved momentum spaces associated to the $\kappa$-deformation of the (3+1) de Sitter and Anti-de Sitter algebras are constructed as orbits of suitable actions of the dual Poisson-Lie group associated to the $\kappa$-deformation with non-vanishing cosmological constant. The $\kappa$-de Sitter and $\kappa$-Anti-de Sitter curved momentum spaces are separately analysed, and they turn out to be, respectively, half of the (6+1)-dimensional de Sitter space and half of a space with $SO(4,4)$ invariance. Such spaces are made of the momenta associated to spacetime translations and the "hyperbolic" momenta associated to boost transformations. The known $\kappa$-Poincar\'e curved momentum space is smoothly recovered as the vanishing cosmological constant limit from both of the constructions.

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Angel Ballesteros, Giulia Gubitosi, Iván Gutiérrez-Sagredo, Francisco J. Herranz. 2017-11-14. Curved momentum spaces from quantum (Anti-)de Sitter groups in (3+1) dimensions. https://doi.org/10.1103/physrevd.97.106024

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