Conformal Symmetry of the Massless Staruszkiewicz Model and the Photon-like Charge Problem

Within classical electrodynamics, the problem of the existence or non-existence of massless charges is commonly associated with the problem of radiation reaction. Here, the relativistic system of two massless charged particles is considered within the Staruszkiewicz model, in which radiation reaction is neglected. The model is formulated in the Hamiltonian form with constraints. The system is invariant with respect to 15-parameter conformal group. The corresponding conserved canonical generators and the relativistic Laplace–Runge–Lenz vector imply the superintegrability of the system. The trajectory of the unbounded relative motion is hyperbolic, as in the non-relativistic Kepler problem. Surprisingly, particle world lines turn out to be lightlike straight rays, as if charges are switched off. Abstract Published by the Jagiellonian University 2026 authors