Triply special relativity

Kowalski-Glikman, Jerzy; Smolin, Lee

doi:10.1103/physrevd.70.065020

Cited by 120 publications

(193 citation statements)

References 34 publications

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“…The Lie form found coincides with that provided by the α 2 deformation above. Furthermore, it was pointed out in [8], that by taking M into account, the "Triply Special Relativity" of [19] is linearized, and the resulting, Lie-type, deformation is the one provided by α 1 above (this was essentially a repeat of Yang's observation on Snyder's proposal, applied to the momentum sector). Thus, it seems that when M is taken into account, non-linear redefinitions bring the "Multi-Special Relativity" algebras into one of the forms found above 13 .…”

Section: Relation With Other Algebrasmentioning

confidence: 98%

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Generalized Quantum Relativistic Kinematics: A Stability Point of View

Chryssomalakos

Okon

2004

Int. J. Mod. Phys. D

111

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We apply Lie algebra deformation theory to the problem of identifying the stable form of the quantum relativistic kinematical algebra. As a warm up, given Galileo's conception of spacetime as input, some modest computer code we wrote zeroes in on the Poincaré-plus-Heisenberg algebra in about a minute. Further ahead, along the same path, lies a three dimensional deformation space, with an instability double cone through its origin. We give physical as well as geometrical arguments supporting our view that moment, rather than position operators, should enter as generators in the Lie algebra. With this identification, the deformation parameters give rise to invariant length and mass scales. Moreover, standard quantum relativistic kinematics of massive, spinless particles corresponds to non-commuting moment operators, a purely quantum effect that bears no relation to spacetime non-commutativity, in sharp contrast to earlier interpretations. 2 C. Chryssomalakos and E. Okon

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Section: Relation With Other Algebrasmentioning

confidence: 98%

“…where [X µ , f (P )] = −i q∂f (P )/∂P µ was used 19 . Notice that the Z-Z non-commutativity is a purely quantum (q = 0) phenomenon and has no connection to spacetime non-commutativity.…”

Section: The Algebra Of Standard Quantum Relativistic Kinematicsmentioning

confidence: 99%

Generalized Quantum Relativistic Kinematics: A Stability Point of View

Chryssomalakos

Okon

2004

Int. J. Mod. Phys. D

111

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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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“…Thus, the inconsistency between the right-and left-hand sides of the Friedmann equation arises when one applies the quantum gravitational effects for the matter content while considering the geometric part to be purely classic. We should therefore explore quantum gravitational effects for the geometric part which support the energy density bound (28) and also entropy bound (25) that we have obtained in the DSR framework. Very interestingly, the modified Friedmann equations that are suggested by loop quantum cosmology (LQC) [36] predict an upper bound for the energy density.…”

Section: Cosmology: Dsr Versus Lqcmentioning

confidence: 99%

Early universe thermostatistics in curved momentum spaces

Gorji¹,

Hosseinzadeh²,

Nozari³

et al. 2016

Phys. Rev. D

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The theories known as doubly special relativity are introduced in order to take into account an observer-independent length scale and the speed of light in the framework of special relativity. These theories can be generally formulated on the de Sitter and also recently proposed anti-de Sitter momentum spaces. In the context of these theories, we study the statistical mechanics and to do this, we consider the natural measure on the corresponding extended phase space. The invariant measure on the space of distinct microstates is obtained by restriction of the natural measure of the extended phase space to the physical phase space through the disintegration theorem. Having the invariant measure, one can study the statistical mechanics in an arbitrary ensemble for any doubly special relativity theory. We use the constructed setup to study the statistical properties of four doubly special relativity models. Applying the results to the case of early universe thermodynamics, we show that one of these models that is defined by the cosmological coordinatization of anti-de Sitter momentum space, implies a finite total number of microstates. Therefore, without attribution to any ensemble density and quite generally, we obtain entropy and internal energy bounds for the early radiation dominated universe. We find that while these results cannot be supported by the standard Friedmann equations, they indeed are in complete agreement with the nonsingular effective Friedmann equations that arise in the context of loop quantum cosmology.

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Triply special relativity

Cited by 120 publications

References 34 publications

Generalized Quantum Relativistic Kinematics: A Stability Point of View

Generalized Quantum Relativistic Kinematics: A Stability Point of View

Kinematics of particles with quantum-de Sitter-inspired symmetries

Early universe thermostatistics in curved momentum spaces

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