scholarly journals CANONICAL REALIZATIONS OF DOUBLY SPECIAL RELATIVITY

2007 ◽  
Vol 16 (07) ◽  
pp. 1133-1147 ◽  
Author(s):  
PABLO GALÁN ◽  
GUILLERMO A. MENA MARUGÁN
Keyword(s):  
Special Relativity ◽  
Lorentz Transformations ◽  
Uncertainty Principles ◽  
Position Space ◽  
Gravity’S Rainbow ◽  
Gravity's Rainbow ◽  
Doubly Special Relativity ◽  
Basic Set ◽  
Canonical Realization ◽  
The Relationship

Doubly special relativity is usually formulated in momentum space, providing the explicit nonlinear action of the Lorentz transformations that incorporates the deformation of boosts. Various proposals have appeared in the literature for the associated realization in position space. While some are based on noncommutative geometries, others respect the compatibility of the space–time coordinates. Among the latter, there exist several proposals that invoke in different ways the completion of the Lorentz transformations into canonical ones in phase space. In this paper, the relationship between all these canonical proposals is clarified, showing that in fact they are equivalent. The generalized uncertainty principles emerging from these canonical realizations are also discussed in detail, studying the possibility of reaching regimes where the behavior of suitable position and momentum variables is classical, and explaining how one can reconstruct a canonical realization of doubly special relativity starting just from a basic set of commutators. In addition, the extension to general relativity is considered, investigating the kind of gravity's rainbow that arises from this canonical realization and comparing it with the gravity's rainbow formalism put forward by Magueijo and Smolin, which was obtained from a commutative but noncanonical realization in position space.

scholarly journals Note on uncertainty relations in doubly special relativity and gravity’s rainbow

2015 ◽  
Vol 30 (33) ◽  
pp. 1550178 ◽  
Author(s):  
Edwin J. Son ◽  
Wontae Kim
Keyword(s):  
Black Hole ◽  
Special Relativity ◽  
Hawking Temperature ◽  
Uncertainty Relations ◽  
Schwarzschild Black Hole ◽  
Commutation Relations ◽  
Gravity’S Rainbow ◽  
Gravity's Rainbow ◽  
Doubly Special Relativity

We present commutation relations depending on the rainbow functions which are slightly different from the well-known results. However, the advantage of these new commutation relations are compatible with the calculation of the Hawking temperature in the rainbow Schwarzschild black hole.

scholarly journals KINEMATICAL SOLUTION OF THE UHE-COSMIC-RAY PUZZLE WITHOUT A PREFERRED CLASS OF INERTIAL OBSERVERS

2003 ◽  
Vol 12 (07) ◽  
pp. 1211-1226 ◽  
Author(s):  
GIOVANNI AMELINO-CAMELIA
Keyword(s):  
Special Relativity ◽  
Particle Physics ◽  
Planck Scale ◽  
Cosmic Ray ◽  
Lorentz Symmetry ◽  
Relativity Theory ◽  
Lorentz Transformations ◽  
Doubly Special Relativity ◽  
Energy Scenario ◽  
Special Relativity Theory

Among the possible explanations for the puzzling observations of cosmic rays above the GZK cutoff there is growing interest in the ones that represent kinematical solutions, based either on general formulations of particle physics with small violations of Lorentz symmetry or on a quantum-gravity-motivated scheme for the breakdown of Lorentz symmetry. An unappealing aspect of these cosmic-ray-puzzle solutions is that they require the existence of a preferred class of inertial observers. Here I propose a new kinematical solution of the cosmic-ray puzzle, which does not require the existence of a preferred class of inertial observers. My proposal is a new example of a type of relativistic theories, the so-called "doubly-special-relativity" theories, which have already been studied extensively over the last two years. The core ingredient of the proposal is a deformation of Lorentz transformations in which also the Planck scale Ep (in addition to the speed-of-light scale c) is described as an invariant. Just like the introduction of the invariant c requires a deformation of the Galileian transformations into the Lorentz transformations, the introduction of the invariant Ep requires a deformation of the Lorentz transformations, but there is no special class of inertial observers. The Pierre Auger Observatory and the GLAST space telescope should play a key role in future developments of these investigations. I also emphasize that the doubly-special-relativity theory here proposed, besides providing a solution for the cosmic-ray puzzle, is also the first doubly-special-relativity theory with a natural description of macroscopic bodies, and may find applications in the context of a recently-proposed dark-energy scenario.

scholarly journals THERMODYNAMICS OF MODIFIED BLACK HOLES FROM GRAVITY'S RAINBOW

2007 ◽  
Vol 22 (36) ◽  
pp. 2749-2756 ◽  
Author(s):  
YI LING ◽  
XIANG LI ◽  
HONGBAO ZHANG
Keyword(s):  
Black Holes ◽  
Special Relativity ◽  
Equivalence Principle ◽  
Dispersion Relations ◽  
Specific Class ◽  
Gravity’S Rainbow ◽  
Modified Dispersion Relations ◽  
Gravity's Rainbow

We study the thermodynamics of modified black holes proposed in the context of gravity's rainbow. A notion of intrinsic temperature and entropy for these black holes is introduced. In particular for a specific class of modified Schwarzschild solutions, their temperature and entropy are obtained and compared with those previously obtained from modified dispersion relations in deformed special relativity. It turns out that the results of these two different strategies coincide, and this may be viewed as a support for the proposal of deformed equivalence principle.

DIRAC EQUATION IN THE MAGUEIJO–SMOLIN APPROACH OF DOUBLY SPECIAL RELATIVITY

2012 ◽  
Vol 27 (07) ◽  
pp. 1250031 ◽  
Author(s):  
Z. BELHADI ◽  
F. MÉNAS ◽  
A. BÉRARD ◽  
P. GOSSELIN ◽  
H. MOHRBACH
Keyword(s):  
Dispersion Relation ◽  
Dirac Equation ◽  
Special Relativity ◽  
Momentum Space ◽  
Correspondence Principle ◽  
Semiclassical Approach ◽  
Position Space ◽  
Doubly Special Relativity ◽  
Depth Study ◽  
Gain Access

We reconsider in details the Dirac equation in the context of the Magueijo–Smolin approach to the Doubly Special Relativity. Starting from the deformed dispersion relation we focus on obtaining a Dirac equation in momentum space, allowing us to achieve a more in-depth study of its semiclassical approach. Finally by means of a "deformed correspondence principle" we gain access to an equation in the position space.

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

HAWKING RADIATION VIA TUNNELING OF MASSIVE PARTICLES FROM A GRAVITY'S RAINBOW

2010 ◽  
Vol 25 (38) ◽  
pp. 3229-3240 ◽  
Author(s):  
CHENG-ZHOU LIU
Keyword(s):  
Black Holes ◽  
Hawking Radiation ◽  
Quantum Effect ◽  
Massive Particle ◽  
Planck Scale ◽  
Gravity’S Rainbow ◽  
Gravity's Rainbow ◽  
Corrected Entropy ◽  
Massive Particles ◽  
Massive Particle Tunneling

In the tunneling framework of Hawking radiation, the quantum tunneling of massive particles in the modified Schwarzschild black holes from gravity's rainbow is investigated. While the massive particle tunneling from the event horizon, the metric fluctuation is taken into account, not only due to energy conservation but also to the Planck scale effect of spacetime. The obtained results show that, the emission rate is related to changes of the black hole's quantum corrected entropies before and after the emission. This implies that, considering the quantum effect of spacetime, information conservation of black holes is probable. Meanwhile, the quantum corrected entropy of the modified black hole is obtained and the leading correction behave as log-area type. And that, the emission spectrum with Planck scale correction is obtained and it deviates from the thermal spectrum.

De Nostalgia

2015 ◽  
Vol 11 (3) ◽  
pp. 395-406
Author(s):  
Friedrich Kittler
Keyword(s):  
Technology Transfer ◽  
Second World War ◽  
Discursive Construction ◽  
World War ◽  
Gravity’S Rainbow ◽  
Gravity's Rainbow ◽  
Complete Destruction ◽  
Second World ◽  
Home Territory

The essay presents a reading of three war-related texts: Friedrich Schiller’s Wilhelm Tell, Heinrich von Kleist’s The Battle of Hermann, and Thomas Pynchon’s Gravity’s Rainbow. Written against the background of the Revolutionary Wars and the Prussian Wars of Liberation, respectively, the plays by Schiller and Kleist engage in the discursive construction of an emphatic sense of heimat (home), either by way of creating the new sentiment of homesickness (originally called nostalgia) or by advocating the complete destruction of the very home territory you are trying to defend. Gravity’s Rainbow, in turn, decodes the Second World War as a massive exercise in technology transfer. It effectively presents a deconstruction of heimat in an age in which the imperative to merge technologies supersedes all national agendas.

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