2004/10/31 by Alexei A. Deriglazov, A. A. Deriglazov, B. F. Rizzuti · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Doubly special relativity #Energy–momentum relation #Four-force #Four-momentum #General relativity #Invariant (physics) #Invariant mass #Lorentz covariance #Lorentz transformation #Mathematical physics #Momentum (technical analysis) #Noncommutative and Quantum Gravity Theories #One-way speed of light #Physics #Position (finance) #Position and momentum space #Principle of relativity #Quantum mechanics #Relativistic mechanics #Special relativity #Theory of relativity #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.71.123515
published as Phys.Rev. D71 (2005) 123515 · Latex twice, 14 pages, revised in accordance with the version publishedin Phys. Rev. D
openalex publication_date 2005/06/09 · arxiv created 2005/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.