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

Abstract

The Carroll group was originally introduced by Lévy-Leblond (1965 Ann. Inst. Henri Poincaré 3 1) by considering the contraction of the Poincaré group as c → 0. In this paper an alternative definition, based on the geometric properties of a non-Minkowskian, non-Galilean but nevertheless boost-invariant, spacetime structure is proposed. A 'duality' with the Galilean limit c → ∞ is established. Our theory is illustrated by Carrollian electromagnetism. © 2014 IOP Publishing Ltd.