Deformed boost transformations that saturate at the Planck scale

Bruno, N. Rossano; Amelino‐Camelia, Giovanni; Kowalski-Glikman, Jerzy

doi:10.1016/s0370-2693(01)01264-3

Cited by 225 publications

(283 citation statements)

References 18 publications

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“…Our method was used in similar context by [15] but with a different representation of κ-Minkowski phase space algebra. Before proceeding to derive the κ-LT for the coordinates x µ , let us first find out the new dispersion law that is κ-LT invariant.…”

Section: Ii: Non-linear κ-Lorentz Transformationsmentioning

confidence: 99%

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Deformed special relativity and deformed symmetries in a canonical framework

Ghosh

Pal²

2007

Phys. Rev. D

108

140

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Abstract:In this paper we have studied the nature of kinematical and dynamical laws in κ-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of κ-Minkowski phase space algebra that yields the κ-extended finite Lorentz transformations derived in [16]. This is a particular form of a Deformed Special Relativity model that admits a modified energy-momentum dispersion law as well as noncommutative κ-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and not κ-Minkowski) phase space algebra and Special Relativity Lorentz transformation (and not κ-extended Lorentz transformation). The complete set of deformed symmetry generators are constructed that obeys an unmodified closed algebra but induce deformations in the symmetry transformations of the physical κ-Minkowski phase space variables. Furthermore, we demonstrate the usefulness and simplicity of this approach through a number of phenomenological applications both in classical and quantum mechanics. We also construct a Lagrangian for the κ-particle.

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Section: Ii: Non-linear κ-Lorentz Transformationsmentioning

confidence: 99%

“…We will start from the infinitesimal κ-LTs induced by Lorentz generators in κ-space by explicit usage of the κ-NC algebra proposed here. The finite κ-LTs will be composed out of them by integration [15]. These specific κ-LTs were first derived in [16] from a different perspective.…”

Section: Introductionmentioning

confidence: 99%

Deformed special relativity and deformed symmetries in a canonical framework

Ghosh

Pal²

2007

Phys. Rev. D

108

140

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“…Modifications of special relativity in which the action of the transformations are non-linear have been considered by a number of authors [30,2,7,13,18,16,17]. To our knowledge the earliest such proposal is by Fock [30] and related proposals have been considered earlier also in [18,17,16,2,7,13]. We consider that our contribution is mainly to take a phenomenological point of view in which we insist that the modifications of special relativity are to be treated in the most general way possible, so as to allow nature to teach us if and how the relativity of inertial frames is realized in a fundamental theory.…”

Section: Introductionmentioning

confidence: 99%

Generalized Lorentz invariance with an invariant energy scale

2003

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The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a non-linear action of the Lorentz transformations on momentum space. Several examples are discussed in which the speed of light varies with energy and elementary particles have a maximum momenta and/or energy. Energy and momentum conservation are suitably generalized and a proposal is made for how the new transformation laws apply to composite systems. We then use these results to explain the ultra high energy cosmic ray anomaly and we find a form of the theory that explains the anomaly, and leads also to a maximum momentum and a speed of light that diverges with energy. We finally propose that the spatial coordinates be identified as the generators of translation in Minkowski spacetime. In some examples this leads to a commutative geometry, but with an energy dependent Planck constant.lsmolin@perimeterinstitute.ca, j.magueijo@ic.ac.uk 1

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“…DSR theories are characterized by the inclusion of a Lorentz invariant energy and/or momentum scale, in addition to the fundamental scale provided by the speed of light [28][29][30][31][32][33][34]. The invariance of this new scale (supposed to be related to the Planck scale) is possible thanks to a nonlinear action of the Lorentz group in momentum space.…”

Section: Doubly Special Relativity and Gravity's Rainbowmentioning

confidence: 99%

“…In addition, one encounters deformed dispersion relations in the so-called doubly special relativity (DSR) theories [28][29][30][31][32][33][34]. The initial motivation for these theories was to solve the apparent inconsistency that exists between the relativity principle and the emergence of a fundamental scale (Planck scale), suggested by most approaches to quantum gravity [35].…”

Section: Introductionmentioning

confidence: 99%

Entropy and temperature of black holes in a gravity’s rainbow

Galán

Marugán

2006

Phys. Rev. D

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The linear relation between the entropy and area of a black hole can be derived from the Heisenberg principle, the energy-momentum dispersion relation of special relativity, and general considerations about black holes. There exist results in quantum gravity and related contexts suggesting the modification of the usual dispersion relation and uncertainty principle. One of these contexts is the gravity's rainbow formalism. We analyze the consequences of such a modification for black hole thermodynamics from the perspective of two distinct rainbow realizations built from doubly special relativity. One is the proposal of Magueijo and Smolin and the other is based on a canonical implementation of doubly special relativity put forward recently by the authors. In these scenarios, we obtain modified expressions for the entropy and temperature of black holes. We show that, for a family of doubly special relativity theories satisfying certain properties, the temperature can vanish in the limit of zero black hole mass. For the Magueijo and Smolin proposal, this is only possible for some restricted class of models with bounded energy and unbounded momentum. With the proposal of a canonical implementation, on the other hand, the temperature may vanish for more general theories; in particular, the momentum may also be bounded, with bounded or unbounded energy. This opens new possibilities for the outcome of black hole evaporation in the framework of a gravity's rainbow.

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Deformed boost transformations that saturate at the Planck scale

Cited by 225 publications

References 18 publications

Deformed special relativity and deformed symmetries in a canonical framework

Deformed special relativity and deformed symmetries in a canonical framework

Generalized Lorentz invariance with an invariant energy scale

Entropy and temperature of black holes in a gravity’s rainbow

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