Related papers: Position space of Doubly Special Relativity
We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently…
We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a…
We propose version of doubly special relativity theory starting from position space. The version is based on deformation of ordinary Lorentz transformations due to the special conformal transformation. There is unique deformation which does…
Authors derive the Lorentz-Einstein transformation for the space-time coordinates starting with a one-space dimension approach. They add to the results the invariance of the space coordinates measured perpendicular to the direction of…
A new relativistic transformation in the velocity space (here named the differential Lorentz transformation) is formulated solely from the principle of relativity and the invariance of the speed of light. The differential Lorentz…
We present and discuss two different possibilities to construct position space version for Magueijo-Smolin (MS) doubly special relativity proposal. The first possibility is to start from ordinary special relativity and then to define…
For a certain example of a "doubly special relativity theory" the modified space-time Lorentz transformations are obtained from momentum space transformations by using canonical methods. In the sequel an energy-momentum dependent space-time…
Doubly Special Relativity is usually formulated in momentum space, providing the explicit nonlinear action of the Lorentz transformations that incorporates the deformation of boosts. Various proposals have appeared in the literature for the…
We discuss a way to obtain the doubly special relativity kinematical rules (the deformed energy-momentum relation and the nonlinear Lorentz transformations of momenta) starting from a singular Lagrangian action of a particle with linearly…
We generate non-linear representations of the Lorentz Group by unitary transformation over the Lorentz generators. To do that we use deformed scale transformations by introducing momentum-depending parameters. The momentum operator…
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…
Lorentz transformation on two-dimensional spacetime is obtained without assumption of linearity. To obtain this, we use the invariance of wave equations, which is recently proved to be equivalent to the causality preservation.
We show that starting with the fact that special relativity theory is concerned with a distortion of the observed length of a moving rod, without mentioning if it is a "contraction" or "dilation", we can derive the Lorentz transformations…
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…
Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x-y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of…
The quaternion spaces can be used to describe the property of electromagnetic field and gravitational field. In the quaternion space, some coordinate transformations can be deduced from the feature of quaternions, including Lorentz…
There are two major alternatives for violating the (usual) Lorentz invariance at large (Planckian) energies or momenta - either not all inertial frames (in the Planck regime) are equivalent (e.g., there is an effectively preferred frame) or…
Starting with two light clocks to derive time dilation expression, as many textbooks do, and then adding a third one, we work on relativistic spacetime coordinates relations for some simple events as emission, reflection and return of light…
The apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not…
The standard approaches of phenomenology of Quantum Gravity have usually explicitly violated Lorentz invariance, either in the dispersion relation or in the addition rule for momenta. We investigate whether it is possible in 3+1 dimensions…