Numerical Evaluation of a Soliton Pair with Long-Range Interaction

We determine the interaction energy of electric monopole pairs, sources and sinks of a Coulombic field. These charges are represented by topological solitons of finite size and mass, described by a field of SO(3) rotations without any divergences. Such monopoles feel, at large distances, a pure Coulombic interaction. A crucial test for the physical interpretation of these monopoles is a classical running of the charge at small distances, expected from the finite soliton size. We investigate in detail a first observation of the increase in the effective charge at distances of a few soliton radii in this purely Coulombic system and compare it with the running of the coupling in perturbative QED.