# Interplay between Spacetime Curvature, Speed of Light and Quantum Deformations of Relativistic Symmetries

@article{Ballesteros2021InterplayBS,
title={Interplay between Spacetime Curvature, Speed of Light and Quantum Deformations of Relativistic Symmetries},
author={Angel Ballesteros and Giulia Gubitosi and Flavio Mercati},
journal={Symmetry},
year={2021},
volume={13},
pages={2099}
}
• Published 10 October 2021
• Physics, Mathematics, Computer Science
• Symmetry
Recent work showed that κ-deformations can describe the quantum deformation of several relativistic models that have been proposed in the context of quantum gravity phenomenology. Starting from the Poincaré algebra of special-relativistic symmetries, one can toggle the curvature parameter Λ, the Planck scale quantum deformation parameter κ and the speed of light parameter c to move to the well-studied κ-Poincaré algebra, the (quantum) (A)dS algebra, the (quantum) Galilei and Carroll algebras…
3 Citations

## Figures and Tables from this paper

Deformed quantum phase spaces, realizations, star products and twists
• Physics, Mathematics
• 2021
We review deformed quantum phase spaces and their realizations in terms of undeformed phase space. In particular, methods of calculation for the star product, coproduct of momenta and twist from
Diffeomorphisms in momentum space: physical implications of different choices of momentum coordinates in the Galilean Snyder model
• Physics
• 2021
It has been pointed out that different choices of momenta can be associated to the same noncommutative spacetime model. The question of whether these momentum spaces, related by diffeomorphisms,
Double Quantization
• Physics
• 2021
In a quantum gravity theory, it is expected that the classical notion of spacetime disappears, leading to a quantum structure with new properties. A possible way to take into account these quantum

## References

SHOWING 1-10 OF 152 REFERENCES
Cayley-Klein Lie Bialgebras: Noncommutative Spaces, Drinfel'd Doubles and Kinematical Applications
• Computer Science, Physics
Symmetry
• 2021
The Cayley–Klein (CK) formalism is applied to the real algebra so(5) by making use of four graded contraction parameters describing, in a unified setting, 81 Lie algebras, which cover the (anti-)de
Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces
• Physics, Mathematics
Journal of Physics A: Mathematical and Theoretical
• 2021
Quantum homogeneous spaces are noncommutative spaces with quantum group covariance. Their semiclassical counterparts are Poisson homogeneous spaces, which are quotient manifolds of Lie groups M = G/H
Fuzzy worldlines with κ-Poincaré symmetries
• Physics, Mathematics
Journal of High Energy Physics
• 2021
Abstract A novel approach to study the properties of models with quantum-deformed relativistic symmetries relies on a noncommutative space of worldlines rather than the usual noncommutative
Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• Physics, Mathematics
Classical and Quantum Gravity
• 2021
The complete classification of classical r-matrices generating quantum deformations of the (3 + 1)-dimensional (A)dS and Poincaré groups such that their Lorentz sector is a quantum subgroup is
Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is
‘A’
• P. Alam
• Composites Engineering: An A–Z Guide
• 2021
‘E’
• P. Alam
• Composites Engineering: An A–Z Guide
• 2021
Dispersion relations in κ-noncommutative cosmology
• Physics, Mathematics
Journal of Cosmology and Astroparticle Physics
• 2020
We study noncommutative deformations of the wave equation in curved backgrounds and discuss the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime.
Fock Space
• An Interpretive Introduction to Quantum Field Theory
• 2020
Four-dimensional gravity on a covariant noncommutative space
• Physics
Journal of High Energy Physics
• 2020
We formulate a model of noncommutative four-dimensional gravity on a covariant fuzzy space based on SO(1,4), that is the fuzzy version of the $\text{dS}_4$. The latter requires the employment of a