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arXiv · 2508.08390

Planons and their Carroll-Galilei symmetries

José Figueroa-O'Farrill·Simon Pekar·Alfredo Pérez·Stefan Prohazka
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Abstract

We study the dynamics of planons, particles whose mobility is restricted to a plane, through the classification of coadjoint orbits and unitary irreducible representations of the centrally extended planon group. Planons are closely related to Galilei/Bargmann symmetries and, remarkably, the often-ignored massless coadjoint orbits of the Galilei group play a central r\^ole in their description. We thereby provide a nontrivial physical interpretation of these orbits. We further construct classical and quantum dipoles as bound states of monopoles, where the restricted planar motion arises from a novel mixed Carroll-Galilei symmetry. We also argue that the simplest and already experimentally realised systems with Carroll symmetry are in crystals.

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José Figueroa-O'Farrill, Simon Pekar, Alfredo Pérez, Stefan Prohazka. 2025-08-11. Planons and their Carroll-Galilei symmetries. https://doi.org/10.1007/jhep11(2025)030

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