Principle of Relativity, Dual Poincaré Group and Relativistic Quadruple
arXiv:0909.5497
Abstract
Based on the principle of relativity with two universal constants (c, l) and in the inertial motion group IM(1,3)\sim PGL(5,R), with Lorentz isotropy, in addition to Poincaré group of Einstein's SR the dual Poincaré group preserves the origin lightcone and its space/time-like region R_\pm appeared at common origin of intersected Minkowski/dS/AdS space. The dual Poincare kinematics is on a pair of degenerate Einstein manifolds with Λ_\pm=\pm3l^{-2} for R_\pm, respectively. Thus, there is a Poincaré double and the dS double for dS/AdS SR. Further, with other four doubles they form a relativistic quadruple for three kinds of SR on M/D_\pm, respectively. The dS SR with the dS-dual Poincare double provides new kinematics for cosmic scale physics.
arXiv comment16 pages. Extended version