scholarly journals CONFORMAL GENERATORS AND DOUBLY SPECIAL RELATIVITY THEORIES

2005 ◽  
Vol 20 (11) ◽  
pp. 861-867 ◽  
Author(s):  
CARLOS LEIVA
Keyword(s):  
Special Relativity ◽  
Linear Combination ◽  
Dimensional Reduction ◽  
Light Cone ◽  
Massless Particle ◽  
Conformal Group ◽  
Cone Structure ◽  
Doubly Special Relativity

In this paper, the relation between the modified Lorenz boosts, proposed in the doubly relativity theories and a linear combination of Conformal Group generators in R1,d-1 is investigated. The introduction of a new generator is proposed in order to deform the Conformal Group to achieve the connection conjectured. The new generator is obtained through a formal dimensional reduction from a free massless particle living in a R2,d space. Due to this treatment it is possible to say that even DSR theories modify light-cone structure in R1,d-1, it could remains, in some cases, untouched in R2,d.

scholarly journals EXTENDED CONFORMAL GROUP AND DSR VELOCITIES ON THE PHYSICAL SURFACE

2006 ◽  
Vol 21 (13n14) ◽  
pp. 2863-2876
Author(s):  
CARLOS LEIVA
Keyword(s):  
Dimensional Reduction ◽  
Relativistic Particle ◽  
Dimensional Space ◽  
Lorentz Invariance ◽  
Conformal Group ◽  
Reduction Procedure ◽  
Doubly Special Relativity ◽  
Nonlinear Algebra ◽  
Space Dynamics ◽  
The One

The relation between conformal generators and Magueijo–Smolin Doubly Special Relativity term, is achieved. Through a dimensional reduction procedure, it is demonstrated that a massless relativistic particle living in a d-dimensional space, is isomorphic to the one living in a d+2 space with pure Lorentz invariance and to a particle living in a AdS d+1 space. To accomplish these identifications, the conformal group is extended and a nonlinear algebra is obtained. Finally, because the relation between momenta and velocities is known through the dimensional reduction procedure, the problem of position space dynamics is solved.

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 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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