Images of the lines under the MS transformations and the Concept of Velocity in the DSR theories
Abstract
The effect of the MaguejoSmolin (MS) transformations on a straight line in the energy momentum space will be studied. We will interpret the slope of this line as velocity $dE/dp$, which can leads to addition rule for the velocities in the MS doubly special relativity (DSR) case. Relation between two expressions $dE/dp$ and $p/E$ for velocity in the momentum space will be investigated more and the energy dependency of the velocities in the DSR theories is related to the geometrical properties of the lines under DSR transformations. The images of two parallel lines under the MS transformations will be studied and we will compute crossing point of these lines under the MS transformations in the energymomentum space. The linearfractional transformations don't keep parallelism. The crossing point is on a line in the energymomentum space with a constant momentum $E_p/c$.
 Publication:

arXiv eprints
 Pub Date:
 January 2015
 arXiv:
 arXiv:1501.07776
 Bibcode:
 2015arXiv150107776J
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 10 pages, 3 figures