scholarly journals Doubly special relativity theories as different bases of κ-Poincaré algebra

2002 ◽  
Vol 539 (1-2) ◽  
pp. 126-132 ◽  
Author(s):  
J Kowalski-Glikman ◽  
S Nowak
Keyword(s):  
Special Relativity ◽  
Doubly Special Relativity ◽  
Poincaré Algebra

scholarly journals DOUBLY SPECIAL RELATIVITY VERSUS κ-DEFORMATION OF RELATIVISTIC KINEMATICS

2003 ◽  
Vol 18 (01) ◽  
pp. 7-18 ◽  
Author(s):  
JERZY LUKIERSKI ◽  
ANATOL NOWICKI
Keyword(s):  
Special Relativity ◽  
Minkowski Space ◽  
Noncommutative Space ◽  
Relativistic Kinematics ◽  
Large Classes ◽  
Doubly Special Relativity ◽  
Deformed Minkowski Space ◽  
Composition Law ◽  
Poincaré Algebra ◽  
The One

We argue that the so-called doubly special relativity (DSR), recently proposed by Amelino-Camelia et al.1,2 with deformed boost transformations identical with the formulae for κ-deformed kinematics in bicrossproduct basis is classical special relativity in nonlinear disguise. The choice of symmetric composition law for deformed four-momenta as advocated in Refs. 1 and 2 implies that DSR is obtained by considering the nonlinear four-momenta basis of classical Poincaré algebra and it does not lead to noncommutative space–time. We also show how to construct two large classes of doubly special relativity theories — generalizing the choice in Refs. 1 and 2 and the one presented by Magueijo and Smolin.3 The older version of deformed relativistic kinematics, differing essentially from classical theory in the coalgebra sector and leading to noncommutative κ-deformed Minkowski space is provided by quantum κ-deformation of Poincaré symmetries.

scholarly journals SCALAR FIELD THEORY ON κ-MINKOWSKI SPACE–TIME AND DOUBLY SPECIAL RELATIVITY

2005 ◽  
Vol 20 (20n21) ◽  
pp. 4925-4940 ◽  
Author(s):  
M. DASZKIEWICZ ◽  
K. IMIŁKOWSKA ◽  
J. KOWALSKI-GLIKMAN ◽  
S. NOWAK
Keyword(s):  
Scalar Field ◽  
Special Relativity ◽  
Minkowski Space ◽  
Space Time ◽  
Doubly Special Relativity ◽  
Minkowski Space Time ◽  
Point Vertex ◽  
Field Action ◽  
Poincaré Algebra ◽  
Energy And Momentum

In this paper we recall the construction of scalar field action on κ-Minkowski space–time and investigate its properties. In particular we show how the coproduct of κ-Poincaré algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space–time, equivalent to the original one. Adding the self-interaction Φ4 term we investigate the modified conservation laws. We show that the local interactions on κ-Minkowski space–time give rise to six inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.

scholarly journals Doubly Special Relativity with Light-Cone Deformation

2003 ◽  
Vol 18 (24) ◽  
pp. 1711-1719 ◽  
Author(s):  
A. Błaut ◽  
M. Daszkiewicz ◽  
J. Kowalski-Glikman
Keyword(s):  
Phase Space ◽  
Special Relativity ◽  
Light Cone ◽  
Relativity Theory ◽  
Two Dimensional ◽  
Standard Quantum ◽  
Doubly Special Relativity ◽  
Poincaré Algebra ◽  
Galilean Symmetry ◽  
Special Relativity Theory

We propose a new Doubly Special Relativity theory based on the generalization of the κ-deformation of the Poincaré algebra acting along one of the null directions. We recall the quantum Hopf structure of such deformed Poincaré algebra and use it to derive the phase space commutation relations. As in the DSR based on the standard quantum κ-Poincaré algebra we find that the spacetime is noncommutative. We investigate the fate of the properties of Special Relativity in the null basis: the split of the algebra of Lorentz and momentum generators into kinematical and dynamical parts, the action of the kinematical boost M+-, and the emergence of the two-dimensional Galilean symmetry.

scholarly journals CLASSICAL VELOCITY IN κ-DEFORMED POINCARÉ ALGEBRA AND A MAXIMUM ACCELERATION

2003 ◽  
Vol 18 (07) ◽  
pp. 527-536 ◽  
Author(s):  
S. KALYANA RAMA
Keyword(s):  
Special Relativity ◽  
Particle Velocity ◽  
Simple Form ◽  
Classical Limit ◽  
Particle Trajectory ◽  
Constant Force ◽  
Maximum Acceleration ◽  
Length Scales ◽  
Doubly Special Relativity ◽  
Poincaré Algebra

We study the commutators of the κ-deformed Poincaré algebra (κPA) in an arbitrary basis. It is known that the two recently studied doubly special relativity theories correspond to different choices of κPA bases. We present another such example. We consider the classical limit of κPA and calculate particle velocity in an arbitrary basis. It has standard properties and its expression takes a simple form in terms of the variables in the Snyder basis. We then study the particle trajectory explicitly for the case of a constant force. Assuming that the spacetime continuum, velocity, acceleration, etc. can be defined only at length scales greater than x min ≠ 0, we show that the acceleration has a finite maximum.

scholarly journals Berry phase effects in the dynamics of Dirac electrons in doubly special relativity framework

2008 ◽  
Vol 660 (3) ◽  
pp. 267-274 ◽  
Author(s):  
Pierre Gosselin ◽  
Alain Bérard ◽  
Hervé Mohrbach ◽  
Subir Ghosh
Keyword(s):  
Special Relativity ◽  
Berry Phase ◽  
Doubly Special Relativity

STATISTICAL ORIGIN OF SPECIAL AND DOUBLY SPECIAL RELATIVITY

2013 ◽  
Vol 23 ◽  
pp. 373-378
Author(s):  
PETR JIZBA ◽  
FABIO SCARDIGLI
Keyword(s):  
Brownian Motion ◽  
Special Relativity ◽  
Coarse Graining ◽  
Relativistic Motion ◽  
Relativistic Dynamics ◽  
Compton Wavelength ◽  
Primitive Concept ◽  
Short Scale ◽  
Doubly Special Relativity ◽  
First Time

We show how a Brownian motion on a short scale can originate a relativistic motion on scales larger than particle's Compton wavelength. Special relativity appears to be not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. Our scheme accommodates easily also the doubly special relativistic dynamics. A previously unsuspected, common statistical origin of the two frameworks is brought to light for the first time.

scholarly journals Black hole thermodynamics under the generalized uncertainty principle and doubly special relativity

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
E Maghsoodi ◽  
H Hassanabadi ◽  
Won Sang Chung
Keyword(s):  
Black Hole ◽  
Thermodynamic Properties ◽  
Special Relativity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Black Hole Thermodynamics ◽  
De Sitter ◽  
Doubly Special Relativity ◽  
Heuristic Analysis ◽  
Horizon Case

Abstract We investigate the effect of the generalized uncertainty principle on the thermodynamic properties of the topological charged black hole in anti-de Sitter space within the framework of doubly special relativity. Our study is based on a heuristic analysis of a particle which is captured by the black hole. We obtain some thermodynamic properties of the black hole including temperature, entropy, and heat capacity in the spherical horizon case.

scholarly journals Doubly-Special Relativity: Facts, Myths and Some Key Open Issues

Symmetry ◽  
2010 ◽  
Vol 2 (1) ◽  
pp. 230-271 ◽  
Author(s):  
Giovanni Amelino-Camelia
Keyword(s):  
Special Relativity ◽  
Doubly Special Relativity ◽  
Open Issues
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