Position space versions of Magueijo-Smolin doubly special relativity proposal and the problem of total momentum

Abstract

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 conserved momentum in special way. It generates MS invariant as well as nonlinear MS transformations on the momentum space, leading to consistent picture for one-particle sector of the theory. The second possibility is based on the following observation. Besides the nonlinear MS transformations, the MS energy-momentum relation is invariant also under some inhomogeneous linear transformations. The latter are induced starting from linearly realized Lorentz group in five-dimensional position space. Particle dynamics and kinematics are formulated starting from the corresponding five-dimensional interval. There is no problem of total momentum in the theory. The formulation admits two observer independent scales, the speed of light, $c$, and $k$ with dimension of velocity. We speculate on different possibilities to relate $k$ with fundamental constants. In particular, expression of $k$ in terms of vacuum energy suggests emergence of (minimum) quantum of mass.

arXiv commentLatex twice, 14 pages, revised in accordance with the version publishedin Phys. Rev. D

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• Gravity's rainbow: a bridge between LQC and DSR
• Approaching Space Time Through Velocity in Doubly Special Relativity
• A spacetime realization of kappa-Poincare algebra
• Undeformed (additive) energy conservation law in Doubly Special Relativity
• Generalization of the Extended Lagrangian Formalism on a Field Theory and Applications
• Equilibrium properties of blackbody radiation with an ultraviolet energy cut-off
• Variational problem for Hamiltonian system on so(k, m) Lie-Poisson manifold and dynamics of semiclassical spin
• Five-Dimensional Mechanics as the Starting Point for the Magueijo-Smolin Doubly Special Relativity
• 5-Dimensional $SO(1,4)$-Invariant Action as an Origin to the Magueijo-Smolin Doubly Special Relativity Proposal
• Towards an Entropic Geometrodynamics of Quantum Particles: Mouths of Casimir Wormholes as Planckeons