Realization of doubly special relativistic symmetries in Finsler geometries

Amelino‐Camelia, Giovanni; Barcaroli, Leonardo; Gubitosi, Giulia; Liberati, Stefano; Loret, Niccoló

doi:10.1103/physrevd.90.125030

Cited by 85 publications

(166 citation statements)

References 48 publications

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“…which leaves the commutation relations (19) invariant and shows that the X a and L a generators can be also interchanged at the dual Lie algebra level.…”

Section: B the Dual Poisson-lie Groupmentioning

confidence: 99%

Curved momentum spaces from quantum (anti–)de Sitter groups in ( 3+1 ) dimensions

et al. 2018

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Curved momentum spaces associated to the κ-deformation of the (3 þ 1) de Sitter and anti-de Sitter algebras are constructed as orbits of suitable actions of the dual Poisson-Lie group associated to the κ-deformation with nonvanishing cosmological constant. The κ-de Sitter and κ-anti-de Sitter curved momentum spaces are separately analyzed, and they turn out to be, respectively, half of the (6 þ 1)-dimensional de Sitter space and half of a space with SOð4; 4Þ invariance. Such spaces are made of the momenta associated to spacetime translations and the "hyperbolic" momenta associated to boost transformations. The known κ-Poincaré curved momentum space is smoothly recovered as the vanishing cosmological constant limit from both of the constructions.

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“…which leaves the commutation relations (19) invariant and shows that the X a and L a generators can be also interchanged at the dual Lie algebra level.…”

Section: B the Dual Poisson-lie Groupmentioning

confidence: 99%

Curved momentum spaces from quantum (anti–)de Sitter groups in ( 3+1 ) dimensions

et al. 2018

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“…The use of Poisson brackets as Lie brackets is justified by the fact that we consider a semiclassical approximation that was successfully used before [26,38,47] in the phenomenological study of the kinematics of particles whose symmetries are inspired by Hopf algebras. Specifically, we are interested in a regime where quantum effects (such as quantum correlations, fuzziness) can be neglected, so that when we talk about particles we are essentially considering classical objects.…”

Section: Introductionmentioning

confidence: 99%

Kinematics of particles with quantum-de Sitter-inspired symmetries

Barcaroli¹,

Gubitosi

2016

Phys. Rev. D

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We present the first detailed study of the kinematics of free relativistic particles whose symmetries are compatible with the ones described by a quantum deformation of the de Sitter algebra, known as q-de Sitter Hopf algebra. In such algebra, the quantum deformation parameter is a function of the Planck length l 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 κ-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 nonzero, effects due to spacetime curvature and nontrivial 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 with spacetime curvature become energy dependent. Also, the energy dependence of the particles' travel times that is usually associated with momentum space nontrivial properties is modified in a curvature-dependent way.

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“…2 In this paper we do not consider a possible role of the curvature of spacetime. A curvature of spacetime compatible with deformed relativistic theories has only recently begun to be explored in connection with Finsler geometries [16] or a Hamiltonian formalism [17]. 3 For recent works using this construction see Ref.…”

Section: A General Model For Photon Time Delays In Noncommutativementioning

confidence: 99%

Does a deformation of special relativity imply energy dependent photon time delays?

Carmona

Cortés

Relancio

2017

Class. Quantum Grav.

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Theoretical arguments in favor of energy dependent photon time delays from a modification of special relativity (SR) have met with recent gamma ray observations that put severe constraints on the scale of such deviations. We review the case of the generality of this theoretical prediction in the case of a deformation of SR and find that, at least in the simple model based on the analysis of photon worldlines which is commonly considered, there are many scenarios compatible with a relativity principle which do not contain a photon time delay. This will be the situation for any modified dispersion relation which reduces to E = | p| for photons, independently of the quantum structure of spacetime. This fact opens up the possibility of a phenomenologically consistent relativistic generalization of SR with a new mass scale many orders of magnitude below the Planck mass.

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Realization of doubly special relativistic symmetries in Finsler geometries

Cited by 85 publications

References 48 publications

Curved momentum spaces from quantum (anti–)de Sitter groups in ( 3+1 ) dimensions

Curved momentum spaces from quantum (anti–)de Sitter groups in ( 3+1 ) dimensions

Kinematics of particles with quantum-de Sitter-inspired symmetries

Does a deformation of special relativity imply energy dependent photon time delays?

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