2016/04/19 by Jerzy Kocik, Kocik, Jerzy · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Mathematics and Applications #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1604.05698
We present a novel representation of the Lorentz group, the geometric version of which uses "reversions" of a sphere while the algebraic version uses pseudounitary 2x2 matrices over complex numbers and quaternions, and Clifford algebras in general. A remarkably simple formula for relativistic composition of velocities and an accompanying geometric construction follows. The method is derived from the diffeomorphisms of the celestial sphere induced by Lorentz boost.