Generalized Lorentz invariance with an invariant energy scale

Magueijo, João; Smolin, Lee

doi:10.1103/physrevd.67.044017

Cited by 663 publications

(855 citation statements)

References 39 publications

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“…It is also worth noticing that by extending our results of section 3 to field theory we could produce models that have some contact with Double Special Relativity (DSR) [20]. We can see that in fact this could be the case because an equation of motion of the form (18) will produce in field theory some sort of deformed dispersion relations that in simple cases have the form of the deformed dispersion relations presented in recent DSR literature.…”

Section: Resultsmentioning

confidence: 99%

Equations of motion, noncommutativity and quantization

Cortese

Garcı́a

2006

Physics Letters A

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We study the relation between a given set of equations of motion in configuration space and a Poisson bracket. A Poisson structure is consistent with the equations of motion if the symplectic form satisfy some consistency conditions. When the symplectic structure is commutative these conditions are the Helmholtz integrability equations for the nonrestricted inverse problem of the calculus of variations [8]. We have found the corresponding consistency conditions for the symplectic noncommutative case.

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Section: Resultsmentioning

confidence: 99%

Equations of motion, noncommutativity and quantization

Cortese

Garcı́a

2006

Physics Letters A

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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%

“…A realization of this kind is obtained via an invertible nonlinear map U between the physical energy-momentum P a : ÿE; p i and the original energy and momentum variables of standard relativity (in Minkowski space) a : ÿ ; i , which are viewed as auxiliary variables [43] (lowercase Latin indices from the beginning and the middle of the alphabet represent Lorentz and flat spatial indices, respectively). Imposing that the action of rotations is not modified, the nonlinear map U is totally determined by two scalar functions g and f [33,44]. Following a notation similar to that of Refs.…”

Section: Doubly Special Relativity and Gravity's Rainbowmentioning

confidence: 99%

“…Let us check now if the conditions demanded on the function H are fulfilled in some of the DSR models that are more often found in the literature (see the appendix for details). The first of these DSR models can be considered the prototype of the DSR2 family [32,33] (i.e., theories with bounded physical energy and momentum). It is seen in the appendix that H ; g = f ; 1 in this model for the MS proposal.…”

Section: B Bound On the Change Of Areamentioning

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%

See 2 more Smart Citations

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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Some features of scattering problem in a κ‐Deformed minkowski spacetime

Khodadi

2016

Annalen der Physik

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The doubly special relativity (DSR) theories are suggested in order to incorporate an observerindependent length scale in special theory of relativity. The Magueijo-Smolin proposal of DSR is realizable through a particular form of the noncommutative (NC) spacetime (known as κ-Minkowski spacetime) in which the Lorentz symmetry is preserved. In this framework, the NC parameter κ provides the origin of natural cutoff energy scale. Using a nonlinear deformed relativistic dispersion relation along with the Lorentz transformations, we investigate some phenomenological facets of two-body collision problem (without creation of new particles) in a κ-Minkowski spacetime. By treating an elastic scattering problem, we study effects of the Planck scale energy cutoff on some relativistic kinematical properties of this scattering problem. The results are challenging in the sense that as soon as one turns on the κ-spacetime extension, the nature of the two-body collision alters from elastic to inelastic one. It is shown also that a significant kinematical variable involving in heavy ion collisions, the rapidity, is not essentially an additive quantity under a sequence of the nonlinear representation of the Lorentz transformations. 4 In the framework of Newtonian kinematics and for the case of two equal masses m1 = m2, the ratio K 1,a K 1,b in terms of ψ results in the simple relation K 1,a K 1,b = cos 2 ψ which the laboratory scattering angle ψ is limited to the interval 0 ≤ ψ ≤ π 2 . For more details one can see "Classical Mechanics" text book such as Ref. [86]. If ψ = 0 then K 1,a K 1,b = 1, namely, no collision takes place since the speed remains constant before and after the collision and no momentum is transferred to particle-2. However, if ψ → π

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Generalized Lorentz invariance with an invariant energy scale

Cited by 663 publications

References 39 publications

Equations of motion, noncommutativity and quantization

Equations of motion, noncommutativity and quantization

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

Some features of scattering problem in a κ‐Deformed minkowski spacetime

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