Dynamics of Carroll Particles

TL;DR

This paper explores the dynamics of Carroll particles, revealing that while free particles are static, interactions and gauge couplings induce non-trivial motion, expanding understanding of Carroll symmetry in particle systems.

Contribution

It demonstrates that interacting Carroll particles and gauge couplings enable non-trivial dynamics, challenging the notion that free Carroll particles are static.

Findings

Interacting Carroll particles exhibit non-trivial dynamics.

Coupling Carroll particles to gauge fields induces motion.

Single Carroll particles can move when coupled to gauge fields.

Abstract

We investigate particles whose dynamics is invariant under the Carroll group. Although a single free such Carroll particle has no non-trivial dynamics (`the Carroll particle does not move') we show that there exists non-trivial dynamics for a set of interacting Carroll particles. Furthermore, we gauge the Carroll algebra and couple the Carroll particle to these gauge fields. It turns out that for such a coupled system even a single Carroll particle can have non-trivial dynamics.