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Jerzy Kowalskiglikman - One of the best experts on this subject based on the ideXlab platform.
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phenomenology of doubly Special Relativity
2005Co-Authors: Giovanni Amelinocamelia, Jerzy Kowalskiglikman, Gianluca Mandanici, Andrea ProcacciniAbstract:Investigations of the possibility that some novel "quantum" properties of space–time might induce a Planck-scale modification of the energy/momentum dispersion relation focused at first on scenarios with Planck-scale violations of Lorentz symmetry, with an associated reduced n-parameter (n<6) rotation-boost symmetry group. More recently several studies have also considered the possibility of a "doubly Special Relativity," in which the modification of the dispersion relation emerges from a framework with both the Planck scale and the speed-of-light scale as characteristic scales of a 6-parameter group of rotation-boost symmetry transformations (a deformation of the Lorentz transformations). For the schemes with broken Lorentz symmetry at the Planck scale there is a large literature on the derivation of experimental limits. Here we show that the analysis of the experimental limits could be significantly different in a doubly-Special-Relativity framework. We find that the study of photon stability, synchrotron radiation, and threshold conditions for particle production in collision processes, the three contexts which are considered as most promising for constraining the broken-Lorentz-symmetry scenario, should not provide significant constraints on a doubly-Special-Relativity parameter space. However, certain types of analyses of gamma-ray bursts should be sensitive to the symmetry deformation. A key element of our study is an observation that removes a possible sign ambiguity for the doubly-Special-Relativity framework. This result also allows us to characterize more sharply the differences between the doubly-Special-Relativity framework and the framework of κ-Poincare Hopf algebras, two frameworks which are often confused with each other in the literature.
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triply Special Relativity
2004Co-Authors: Jerzy Kowalskiglikman, Lee SmolinAbstract:We describe an extension of Special Relativity characterized by three invariant scales, the speed of light $c$, a mass $\ensuremath{\kappa}$, and a length $R$. This is defined by a nonlinear extension of the Poincar\'e algebra $\mathcal{A}$, which we describe here. For $R\ensuremath{\rightarrow}\ensuremath{\infty}$, $\mathcal{A}$ becomes the Snyder presentation of the $\ensuremath{\kappa}$-Poincar\'e algebra, while for $\ensuremath{\kappa}\ensuremath{\rightarrow}\ensuremath{\infty}$ it becomes the phase space algebra of a particle in de Sitter spacetime. We conjecture that the algebra is relevant for the low energy behavior of quantum gravity, with $\ensuremath{\kappa}$ taken to be the Planck mass, for the case of a nonzero cosmological constant $\ensuremath{\Lambda}={R}^{\ensuremath{-}2}$. We study the modifications of particle motion which follow if the algebra is taken to define the Poisson structure of the phase space of a relativistic particle.
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introduction to doubly Special Relativity
2004Co-Authors: Jerzy KowalskiglikmanAbstract:In these notes, based on the lectures given at 40th Winter School on Theoretical Physics, I review some aspects of Doubly Special Relativity (DSR). In particular, I discuss relation between DSR and quantum gravity, the formal structure of DSR proposal based on $\kappa$-Poincar\'e algebra and non-commutative $\kappa$-Minkowski space-time, as well us some results and puzzles related to DSR phenomenology.
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2 1 gravity and doubly Special Relativity
2004Co-Authors: Jerzy Kowalskiglikman, Lee Smolin, Laurent FreidelAbstract:It is shown that gravity in 2+1 dimensions coupled to point particles provides a nontrivial example of doubly Special Relativity (DSR). This result is obtained by interpretation of previous results in the field and by exhibiting an explicit transformation between the phase space algebra for one particle in 2+1 gravity found by Matschull and Welling and the corresponding DSR algebra. The identification of 2+1 gravity as a DSR system answers a number of questions concerning the latter, and resolves the ambiguity of the basis of the algebra of observables. Based on this observation a heuristic argument is made that the algebra of symmetries of ultra high energy particle kinematics in 3+1 dimensions is described by some DSR theory.
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phenomenology of doubly Special Relativity
2003Co-Authors: Giovanni Amelinocamelia, Jerzy Kowalskiglikman, Gianluca Mandanici, Andrea ProcacciniAbstract:Investigations of the possibility that some novel ``quantum" properties of spacetime might induce a modification dispersion relation focused at first on scenarios with Planck-scale violations of Lorentz symmetry. More recently several studies have considered the possibility of a ``doubly Special Relativity", in which the modification of the dispersion relation emerges from a framework with both the Planck scale and the speed-of-light scale as characteristic scales of a deformation of the Lorentz transformations. For the schemes with broken Lorentz symmetry at the Planck scale there is a large literature on the derivation of experimental limits. We provide here a corresponding analysis for the doubly-Special-Relativity framework. We find that the analyses of photon stability, synchrotron radiation, and threshold conditions for particle production in collision processes, the three contexts which are considered as most promising for constraining the broken-Lorentz-symmetry scenario, cannot provide significant constraints on doubly-Special-Relativity parameter space. However, certain types of analyses of gamma-ray bursts are sensitive to the symmetry deformation. A key element of our study is an observation that removes a possible sign ambiguity for the doubly-Special-Relativity framework. This result also allows us to characterize more sharply the differences between the doubly-Special-Relativity framework and the framework of k-Poincare Hopf algebras, two frameworks which are often confused with each other in the literature.
Sebastian Nowak - One of the best experts on this subject based on the ideXlab platform.
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doubly Special Relativity and de sitter space
2003Co-Authors: Jerzy Kowalskiglikman, Sebastian NowakAbstract:In this paper we recall the construction of Doubly Special Relativity (DSR) as a theory with energy-momentum space being the four dimensional de Sitter space. Then the bases of the DSR theory can be understood as different coordinate systems on this space. We investigate the emerging geometrical picture of Doubly Special Relativity by presenting the basis independent features of DSR that include the non-commutative structure of space-time and the phase space algebra. Next we investigate the relation between our geometric formulation and the one based on quantum $\kappa$-deformations of the Poincar\'e algebra. Finally we re-derive the five-dimensional differential calculus using the geometric method, and use it to write down the deformed Klein-Gordon equation and to analyze its plane wave solutions.
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non commutative space time of doubly Special Relativity theories
2003Co-Authors: Jerzy Kowalskiglikman, Sebastian NowakAbstract:Doubly Special Relativity (DSR) theory is a recently proposed theory with two observer-independent scales (of velocity and mass), which is to describe a kinematic structure underlining the theory of Quantum Gravity. We observe that there are infinitely many DSR constructions of the energy–momentum sector, each of whose can be promoted to the κ-Poincare quantum (Hopf) algebra. Then we use the co-product of this algebra and the Heisenberg double construction of κ-deformed phase space in order to derive the non-commutative space–time structure and the description of the whole of DSR phase space. Next we show that contrary to the ambiguous structure of the energy momentum sector, the space–time of the DSR theory is unique and related to the theory with non-commutative space–time proposed long ago by Snyder. This theory provides non-commutative version of Minkowski space–time enjoying ordinary Lorentz symmetry. It turns out that when one builds a natural phase space on this space–time, its intrinsic length par...
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doubly Special Relativity theories as different bases of κ poincare algebra
2002Co-Authors: Jerzy Kowalskiglikman, Sebastian NowakAbstract:Abstract Doubly Special Relativity (DSR) theory is a theory with two observer-independent scales, of velocity and mass (or length). Such a theory has been proposed by Amelino-Camelia as a kinematic structure which may underline quantum theory of Relativity. Recently another theory of this kind has been proposed by Magueijo and Smolin. In this Letter we show that both these theories can be understood as particular bases of the κ -Poincare theory based on quantum (Hopf) algebra. This observation makes it possible to construct the space–time sector of Magueijo and Smolin DSR. We also show how this construction can be extended to the whole class of DSRs. It turns out that for all such theories the structure of space–time commutators is the same. This results lead us to the claim that physical predictions of properly defined DSR theory should be independent of the choice of basis.
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non commutative space time of doubly Special Relativity theories
2002Co-Authors: Jerzy Kowalskiglikman, Sebastian NowakAbstract:Doubly Special Relativity (DSR) theory is a recently proposed theory with two observer-independent scales (of velocity and mass), which is to describe a kinematic structure underlining the theory of Quantum Gravity. We observe that there is infinitely many DSR constructions of the energy-momentum sector, each of whose can be promoted to the $\kappa$-Poincar\'e quantum (Hopf) algebra. Then we use the co-product of this algebra and the known construction of $\kappa$-deformed phase space via Heisenberg double in order to derive the non-commutative space-time structure and description of the whole of the DSR phase space. Next we show that contrary to the ambiguous structure of the energy momentum sector, the space-time of the DSR theory is unique and equivalent to the theory with non-commutative space-time proposed long ago by Snyder. This theory provides non-commutative version of Minkowski space-time enjoying ordinary Lorentz symmetry. It turns out that when one builds a natural phase space on this space-time, its intrinsic length parameter $\ell$ becomes observer-independent.
J G Pereira - One of the best experts on this subject based on the ideXlab platform.
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de sitter Special Relativity
2007Co-Authors: R Aldrovandi, J Beltran P Almeida, J G PereiraAbstract:A Special Relativity based on the de Sitter group is introduced, which is a theory that might hold up in the presence of a non-vanishing cosmological constant. Like ordinary Special Relativity, it retains the quotient character of spacetime, and a notion of homogeneity. As a consequence, the underlying spacetime will be a de Sitter spacetime, whose associated kinematics will differ from that of ordinary Special Relativity. The corresponding modified notions of energy and momentum are obtained, and the exact relationship between them, which is invariant under a re-scaling of the involved quantities, explicitly exhibited. Since the de Sitter group can be considered a particular deformation of the Poincare group, this theory turns out to be a specific kind of deformed (or doubly) Special Relativity. Some experimental consequences, as well as the causal structure of spacetime—modified by the presence of the de Sitter horizon—are briefly discussed.
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de sitter Special Relativity
2006Co-Authors: R Aldrovandi, J Beltran P Almeida, J G PereiraAbstract:A Special Relativity based on the de Sitter group is introduced, which is the theory that might hold up in the presence of a non-vanishing cosmological constant. Like ordinary Special Relativity, it retains the quotient character of spacetime, and a notion of homogeneity. As a consequence, the underlying spacetime will be a de Sitter spacetime, whose associated kinematics will differ from that of ordinary Special Relativity. The corresponding modified notions of energy and momentum are obtained, and the exact relationship between them, which is invariant under a re-scaling of the involved quantities, explicitly exhibited. Since the de Sitter group can be considered a particular deformation of the Poincar\'e group, this theory turns out to be a specific kind of deformed (or doubly) Special Relativity. Some experimental consequences, as well as the causal structure of spacetime--modified by the presence of the de Sitter horizon--are briefly discussed.
Bin Zhou - One of the best experts on this subject based on the ideXlab platform.
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snyder s model de sitter Special Relativity duality and de sitter gravity
2007Co-Authors: Hanying Guo, Chao-guang Huang, Yu Tian, Bin ZhouAbstract:Between Snyder's quantized space-time model in de Sitter space of momenta and the dS Special Relativity on dS-spacetime of radius R with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with the Planck length lP, R (3/Λ)1/2 should be a fundamental constant. They lead to a dimensionless constant g ~ lPR−1 = (Gc−3Λ/3)1/2 ~ 10−61. These indicate that physics at these two scales should be dual to each other and there is in-between gravity of local dS-invariance characterized by g. A simple model of dS-gravity with a gauge-like action on umbilical manifolds may show these characteristics. It can pass the observation tests and support the duality.
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snyder s model de sitter Special Relativity duality and de sitter gravity
2007Co-Authors: Hanying Guo, Chao-guang Huang, Yu Tian, Bin ZhouAbstract:Between Snyder's quantized space-time model in de Sitter space of momenta and the \dS Special Relativity on \dS-spacetime of radius $R$ with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with Planck length $\ell_P$, $R\simeq (3/\Lambda)^{1/2}$ should be a fundamental constant. They lead to a dimensionless constant $g{\sim\ell_PR^{-1}}=(G\hbar c^{-3}\Lambda/3)^{1/2}\sim 10^{-61}$. These indicate that physics at these two scales should be dual to each other and there is in-between gravity of local \dS-invariance characterized by $g$. A simple model of \dS-gravity with a gauge-like action on umbilical manifolds may show these characters. It can pass the observation tests and support the duality.
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On Special Relativity with cosmological constant
2004Co-Authors: Chao-guang Huang, Zhan Xu, Bin ZhouAbstract:Based on the principle of Relativity and the postulate of invariant speed and length, we propose the theory of Special Relativity with cosmological constant SRc, R, in which the cosmological constant is linked with the invariant length. Its relation with the doubly Special Relativity is briefly mentioned. (C) 2004 Elsevier B.V. All rights reserved.
Stephen M. Barnett - One of the best experts on this subject based on the ideXlab platform.
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Comment on “Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation”
2013Co-Authors: Stephen M. BarnettAbstract:This editorial discusses "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation".
