Related papers: Doubly Special Relativity with light-cone deformat…
We unify kappa-Minkowki spacetime and Lorentz algebra in unique Lie algebra. Introducing commutative momenta, a family of kappa-deformed Heisenberg algebras and kappa-deformed Poincare algebras are defined. They are specified by the matrix…
Within the approach to doubly special relativity (DSR) suggested by Magueijo and Smolin, a new algebraically justified rule of so-called $\kappa$-addition for the energies of identical particles is proposed. This rule permits to introduce…
The $\kappa$-deformed $D=4$ Poincar{\'e} superalgebra written in Hopf superalgebra form is transformed to the basis with classical Lorentz subalgebra generators. We show that in such a basis the $\kappa$-deformed $D=4$ Poincare superalgebra…
We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant $\Lambda$. In…
Hopf algebra methods are applied to study Drinfeld twists of (3+1)-diffeomorphisms and deformed general relativity on \emph{commutative} manifolds. A classical nonlocality length scale is produced above which microcausality emerges. Matter…
The $(4+4)$-dimensional $\kappa$-deformed quantum phase space as well as its $(10+10)$-dimensional covariant extension by the Lorentz sector can be described as Heisenberg doubles: the $(10+10)$-dimensional quantum phase space is the double…
We investigate the properties of kappa-Minkowski spacetime by using representations of the corresponding deformed algebra in terms of undeformed Heisenberg-Weyl algebra. The deformed algebra consists of kappa-Poincare algebra extended with…
The deformed Dirac equation invariant under the $\kappa$-Poincar\'{e}-Hopf quantum algebra in the context of minimal and scalar couplings under spin and pseudospin symmetries limits is considered. The $\kappa$-deformed Pauli-Dirac…
We show that Doubly Special Relativity (DSR) can be viewed as a theory with energy-momentum space being the four dimensional de Sitter space. Different formulations (bases) of the DSR theory considered so far can be therefore understood as…
We propose a new interpretation of doubly special relativity (DSR) based on the distinction between the momentum and the translation generators in its phase space realization. We also argue that the implementation of DSR theories does not…
A deformation of special relativity based on a dispersion relation with an energy independent speed of light and a symmetry between positive and negative energy states is proposed. The deformed Lorentz transformations, generators and…
Doubly special relativity (DSR) introduces an observer-independent energy scale while preserving a deformed relativistic notion of covariance. In many realizations, this leads to an energy-dependent speed of light (light-speed variation,…
We present the generalisation to (3+1) dimensions of a quantum deformation of the (2+1) (Anti)-de Sitter and Poincar\'e Lie algebras that is compatible with the conditions imposed by the Chern-Simons formulation of (2+1) gravity. Since such…
In this paper, we present the results of our investigation relating particle dynamics and non-commutativity of space-time by using Dirac's constraint analysis. In this study, we re-parameterise the time $t=t(\tau)$ along with $x=x(\tau)$…
We consider the simplest class of Lie-algebraic deformations of space-time algebra, with the selection of $\kappa$-deformations as providing quantum deformation of relativistic framework. We recall that the $\kappa$-deformation along any…
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…
Over the last decade there were significant advances in the understanding of quantum gravity coupled to point particles in 3D (2+1-dimensional) spacetime. Most notably it is emerging that the theory can be effectively described as a theory…
Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie…
In deformed or doubly special relativity (DSR) the action of the lorentz group on momentum eigenstates is deformed to preserve a maximal momenta or minimal length, supposed equal to the Planck length. The classical and quantum dynamics of a…
We investigate a quantum geometric space in the context of what could be considered an emerging effective theory from Quantum Gravity. Specifically we consider a two-parameter class of twisted Poincar\'e algebras, from which Lie-algebraic…