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

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 $\kappa$-Poincaré curved momentum space is smoothly recovered as the vanishing cosmological constant limit from both of the constructions.

v2: Version accepted for publication on Phys. Rev. D

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• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Physical Constraints on Quantum Deformations of Spacetime Symmetries
• Effects of Planck-scale-modified dispersion relations on the thermodynamics of charged black holes
• Relativistic compatibility of the interacting $\kappa$-Poincaré model and implications for the relative locality framework
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
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• All noncommutative spaces of $\kappa$-Poincaré geodesics
• Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces
• $\kappa$-Galilean and $\kappa$-Carrollian noncommutative spaces of worldlines
• Fuzzy worldlines with $\kappa$-Poincaré symmetries