Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time

Abstract

The Carroll group was originally introduced by Levy-Leblond [1] by considering the limit of the Poincaré group as $c\to 0$. In this paper an alternative definition, based on the geometric properties of a non-Minkowskian, non-Galilean but nevertheless boost-invariant, space-time structure is proposed. A "duality" with the Galilean limit $c\to \infty$ is established. Our theory is illustrated by Carrollian electromagnetism.

arXiv comment32 pages, no figures. A minor error corrected. Accepted for publication in Classical and Quantum Gravity

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