A Dynamical Approach to Compactify the Three Dimensional Lorentz Group

Marcos Salvai

Abstract: The Lorentz group acts on the projectivized light cone in the three dimensional Lorentz space as the group $G$ of Möbius transformations of the circle. We find the closure of $G$ in the space of all measurable functions of the circle into itself, obtaining a compactification of it as an open dense subset of the three-sphere, with a dynamical meaning related to generalized flows.

Keywords: compactification, Lorentz group, Möbius transformation, generalized flow

Classification (MSC2000): 53C22, 57S20, 58D15, 74A05

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