Kinematics of particles with quantum de Sitter symmetries

Abstract

We present the first detailed study of the kinematics of free relativistic particles whose symmetries are described by a quantum deformation of the de Sitter algebra, known as $q$-de Sitter Hopf algebra. The quantum deformation parameter is a function of the Planck length $\ell$ and the de Sitter radius $H^{-1}$, such that when the Planck length vanishes, the algebra reduces to the de Sitter algebra, while when the de Sitter radius is sent to infinity one recovers the $\kappa$-Poincaré Hopf algebra. In the first limit the picture is that of a particle with trivial momentum space geometry moving on de Sitter spacetime, in the second one the picture is that of a particle with de Sitter momentum space geometry moving on Minkowski spacetime. When both the Planck length and the inverse of the de Sitter radius are non-zero, effects due to spacetime curvature and non-trivial momentum space geometry are both present and affect each other. The particles' motion is then described in a full phase space picture. We find that redshift effects that are usually associated to spacetime curvature become energy-dependent. Also, the energy dependence of particles' travel times that is usually associated to momentum space non-trivial properties is modified in a curvature-dependent way.

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Cited by in corpus (17)

• Investigation on Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case
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• Redshift and lateshift from homogeneous and isotropic modified dispersion relations
• Deformed relativity symmetries and the local structure of spacetime
• Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
• The kappa-(A)dS quantum algebra in (3+1) dimensions
• Deformed relativistic kinematics on curved spacetime -- a geometric approach
• Curved momentum spaces from quantum (Anti-)de Sitter groups in (3+1) dimensions
• The $\kappa$-Newtonian and $\kappa$-Carrollian algebras and their noncommutative spacetimes
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Relativistic compatibility of the interacting $\kappa$-Poincaré model and implications for the relative locality framework
• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Linear Canonical Transformations in Relativistic Quantum Physics
• Quantum groups and noncommutative spacetimes with cosmological constant
• DSR-relativistic spacetime picture and the phenomenology of Planck-scale-modified time dilation
• The universe is not a Lie, but actually an Hopf, algebra