Related papers: Doubly-Special Relativity: Facts, Myths and Some K…
We propose a general framework to describe Planckian deviations from Special Relativity (SR) compatible with a relativistic principle. They are introduced as the leading corrections in an asymptotic approach to SR going beyond the energy…
This work explores the two-dimensional Dirac oscillator (DO) within the framework of Amelino-Camelia doubly special relativity (DSR), employing a modified Dirac equation that preserves the first-order nature of the relativistic wave…
The interest of part of the quantum-gravity community in the possibility of Planck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective,…
Based on the principle of relativity and the postulate of invariant speed and length, we propose the theory of special relativity with cosmological constant ${\cal SR}_{c,R}$ if the invariant length whose square is the inverse of the…
The notions of "motion" and "conserved quantities", if applied to extended objects, are already quite non-trivial in Special Relativity. This contribution is meant to remind us on all the relevant mathematical structures and constructions…
The phase space of a classical particle in DSR contains de Sitter space as the space of momenta. We start from the standard relativistic particle in five dimensions with an extra constraint and reduce it to four dimensional DSR by imposing…
Three related topics are discussed to show the "simplicity, harmony and beauty" of the theory of special relativity (SR): (1) How can de'Broglie discover his famous relation between the particle's momentum and a wave length -- a paradox…
We argue that existing doubly special relativities may not be operationally distinguishable from the special relativity. In the process we point out that some of the phenomenologically motivated modifications of dispersion relations, and…
It is shown how a Doubly-Special Relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a one-dimensional automaton that spawns the Dirac…
Very Special Relativity (VSR) framework, proposed by Cohen and Glashow [1], demonstrated that a proper subgroup of the Poincar\'e group, (in particular ISIM(2)), is sufficient to describe the spacetime symmetries of the so far observed…
We discuss the definition of velocity as dE/dp, where E,p are the energy and momentum of a particle, in Doubly Special Relativity (DSR). If this definition matches dx/dt appropriate for the space-time sector, then space-time can in…
We study the $(1+1)$-dimensional Dirac oscillator within a class of doubly special relativity (DSR) models generated by linear-fractional (projective) transformations on momentum space that preserve both the invariant speed of light and a…
We examine the (2+1)-dimensional Dirac equation in a homogeneous magnetic field under the non-relativistic anti-Snyder model which is relevant to deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum…
An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a…
The study of phase-space constructions based on the properties of the $\kappa$-Poincar\'e Hopf algebra has been a very active area, mostly because of its possible applications in the phenomenology of Planck-scale-induced momentum dependence…
The major extant relativity theories - Galileo's Relativity (GaR), Lorentz's Relativity (LR) and Einstein's Special Relativity (SR), with the latter much celebrated, while the LR is essentially ignored. Indeed it is often incorrectly…
We introduce the Poincar\'e-de Sitter flow with real numbers $\{r,s\}$ to parameterize the relativistic quadruple ${\frak Q}_{PoR}=[{\cal P}, {\cal P}_2, {\cal D}_+,{\cal D}_-]_{M/M_\pm/D_\pm}$ for the triple of Poincar\'e/\dS/\AdS\ group…
In the first part of the thesis we focus on local symmetries. We review a self-consistent framework that we employed in order to discuss the dynamics of the theories of interest. Its merit lies in that we can make the symmetry group act…
A common misconception is that Lorentz invariance is inconsistent with a discrete spacetime structure and a minimal length: under Lorentz contraction, a Planck length ruler would be seen as smaller by a boosted observer. We argue that in…
In this article, we discuss some well-known theoretical models where an observer-independent energy scale or a length scale is present. The presence of this invariant scale necessarily deforms the Lorentz symmetry. We study different…