Doubly Special Relativity: A New Relativity or Not?

Double Special Relativity theories are the relativistic theories in which the transformations between inertial observers are characterized by two observer-independent scales of the light speed and the Planck length. We study two main examples of these theories and want to show that these theories are not the new theories of relativity, but only are re-descriptions of Einstein's special relativity in the non-conventional coordinates.Comment: 5 pages, 1 figures, to appear in proceedings of ERE2005, the XXVIII Spanish Relativity Meeting, Oviedo, Spai

Poisson structure on a space with linear SU(2) fuzziness

The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which the counterpart of the angular momentum, as well as the Euler parameterization of the phase space are introduced. SU(2)-invariant classical systems are discussed, and it is observed that the path of particle can be obtained by the solution of a first-order equation, as the case with such models on commutative spaces. The examples of free particle, rotationally-invariant potentials, and specially the isotropic harmonic oscillator are investigated in more detail.Comment: 12+1 pages, no figs, LaTeX2