Two interacting conformal Carroll particles

In this note we analyse two different models of two interacting conformal Carroll particles that can be obtained as the Carrollian limit of two relativistic conformal particles. The first model describes particles with zero velocity and exhibits infinite dimensional symmetries which are reminiscent of the BMS symmetries. A second model of interaction of Carrollian particles is proposed, where the particles have non zero velocity and therefore, as a consequence of the limit c to 0, are tachyons. Infinite dimensional symmetries are present also in this model.