Dynamics of Carroll particles

We investigate particles whose dynamics are 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 non-trivial dynamics exists 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.