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Poincare, Relativity, Billiards and Symmetry

Thibault Damour
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Abstract

This review is made of two parts which are related to Poincaré in different ways. The first part reviews the work of Poincaré on the Theory of (Special) Relativity. One emphasizes both the remarkable achievements of Poincaré, and the fact that he never came close to what is the essential conceptual achievement of Einstein: changing the concept of time. The second part reviews a topic which probably would have appealed to Poincaré because it involves several mathematical structures he worked on: chaotic dynamics, discrete reflection groups, and Lobachevskii space. This topic is the hidden role of Kac-Moody algebras in the billiard description of the asymptotic behaviour of certain Einstein-matter systems near a cosmological singularity. Of particular interest are the Einstein-matter systems arising in the low-energy limit of superstring theory. These systems seem to exhibit the highest-rank hyperbolic Kac-Moody algebras, and notably E(10), as hidden symmetries.

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Thibault Damour. 2005-01-20. Poincare, Relativity, Billiards and Symmetry. https://arxiv.org/abs/hep-th/0501168

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