Hyperboloid preservation implies the Lorentz and Poincaré groups without dilations

Details Hyperboloid preservation implies the Lorentz and Poincaré groups without dilations Hyperboloid preservation implies the Lorentz and Poincaré groups without dilations

2010-09-20

arxiv.org/abs/1009.3910v1

Physics

Mathematical Physics

12 pages

Scientific paper

An analogue of the Alexandrov-Zeeman theorem, based on hyperboloid preservation, as opposed to light cone preservation, is provided. This characterizes exactly the Poincar\'e group, as opposed to the Poincar\'e group extended by dilations. The hyperbolic analogue, as opposed to the cone-based Alexandrov-Zeeman theorem, is also valid in the case of a single space dimension. An orthochronous version also holds, based on the preservation of forward hyperboloid shells.

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