English

Cromlech, menhirs and celestial sphere: an unusual representation of the Lorentz group

Mathematical Physics 2016-04-20 v1 math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.1604.05698,
  title  = {Cromlech, menhirs and celestial sphere: an unusual representation of the Lorentz group},
  author = {Jerzy Kocik},
  journal= {arXiv preprint arXiv:1604.05698},
  year   = {2016}
}

Comments

29 pages, 25 figures