Dynamics of Carroll Particles

TL;DR

This work investigates Carroll-invariant particle dynamics, showing that a single free Carroll particle does not move, but non-trivial dynamics emerge in interacting two-body systems and when the Carroll algebra is gauged. By taking the Carroll limit of a two-particle relativistic model, the authors derive Carroll-invariant mass-shell constraints and analyze the resulting dynamics, highlighting a conserved center-of-mass quantity but non-trivial motion of constituents. They also gauge the Carroll algebra, introduce Carroll background fields, and construct a covariant particle action that yields dynamics in non-trivial backgrounds, while noting structural differences from Galilei/Bargmann gauging. The study connects Carroll symmetries to broader themes such as BMS algebra and flat-space holography, and suggests future directions toward Carroll gravity and extended objects.

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.