Doubly special relativity in de Sitter spacetime

Mignemi, Salvatore

doi:10.1002/andp.201000105

Cited by 46 publications

(45 citation statements)

References 34 publications

(74 reference statements)

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“…The range of definition of the coordinates depends therefore on the value of the momentum. A possible interpretation of this fact is that the radius of the pseudosphere is a function of the momentum of the particle: this situation is common in DSR theories defined in curved spaces, where the metric properties are momentum dependent [19,14].…”

Section: The Modelmentioning

confidence: 99%

Classical and quantum mechanics of the nonrelativistic Snyder model in curved space

Mignemi¹

2012

Class. Quantum Grav.

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The Snyder-de Sitter (SdS) model is a generalization of the Snyder model to a spacetime background of constant curvature. It is an example of noncommutative spacetime admitting two fundamental scales besides the speed of light, and is invariant under the action of the de Sitter group. Here we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to a three-dimensional sphere, and the related model obtained by considering the anti-Snyder model on a pseudosphere, that we call anti-Snyder-de Sitter (aSdS).By means of a nonlinear transformation relating the SdS phase space variables to canonical ones, we are able to investigate the classical and the quantum mechanics of a free particle and of an oscillator in this framework. As in their flat space limit, the SdS and aSdS models exhibit rather different properties. In the SdS case, a lower bound on the localization in position and momentum space arises, which is not present in the aSdS model. In the aSdS case, instead, a specific combination of position and momentum coordinates cannot exceed a constant value.We explicitly solve the classical and the quantum equations for the motion of the free particle and of the harmonic oscillator. In both the SdS and aSdS cases, the frequency of the harmonic oscillator acquires a dependence on the energy. P.A.C.S. Numbers:

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Section: The Modelmentioning

confidence: 99%

Classical and quantum mechanics of the nonrelativistic Snyder model in curved space

Mignemi¹

2012

Class. Quantum Grav.

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“…1 Despite the fact that most of the research on relativistically compatible deformations of particles' kinematics focuses on cases where spacetime is flat, as mentioned before the best opportunities for phenomenology are found in contexts where spacetime curvature should not be neglected. Only very recently, after early attempts [33][34][35][36] that were however lacking a full understanding of the relative-locality effects produced by momentum space curvature [29][30][31], there have been some proposals to coherently describe nontrivial momentum space properties alongside curvature of spacetime in a relativistic way. Some [37][38][39] have focused on finding an appropriate geometrical description of phase space.…”

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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“…Since the de Sitter manifold is maximally symmetric, it has been viewed as a natural extension for special relativity for the case of non-vanishing cosmological constant. [1,2,3] The free field theory on this manifold is relatively well known, expressed in several charts, and for different spins. [4,5,6,7] However, the opinions on how to build a correct interacting quantum field theory vastly differ.…”

Section: Introductionmentioning

confidence: 99%

“…[2,13] But the de Sitter quantities -at least the observable ones -must reduce, in the case when the cosmological constant vanishes to their Minkowksian counterparts, which can be verified by experiment. Also, the symmetry group reduces from the de Sitter group SO (1,4) to the Poincaré group via the Inönü-Wigner contraction. Even the wavefunctions of matter fields, which are not observable quantities, can be made to match, in some circumstances.…”

Section: Introductionmentioning

confidence: 99%

On the Rest and Flat Limits of the Scalar Modes on the De Sitter Spacetime

2013

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The scalar mode functions on the spatially flat FLRW chart of the de Sitter spacetime are redefined in order to obtain a natural frequencies separation in the special local charts where the momentum vanishes, called here (natural) rest frames. This can be done since in such frames the mode functions are eigenfunctions of the energy operator. Moreover, the most general criteria for choosing the suitable phase factors of the mode functions able to simultaneously determine the correct rest and flat limits are established. These results are compared to the different original choices from the literature.Pacs: 04.62.+v

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Doubly special relativity in de Sitter spacetime

Cited by 46 publications

References 34 publications

Classical and quantum mechanics of the nonrelativistic Snyder model in curved space

Classical and quantum mechanics of the nonrelativistic Snyder model in curved space

Kinematics of particles with quantum-de Sitter-inspired symmetries

On the Rest and Flat Limits of the Scalar Modes on the De Sitter Spacetime

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