Numerical Evaluation of a Soliton Pair with Long Range Interaction

We determine the interaction energy of electric or magnetic monopole pairs, sources and sinks of a Coulombic field. The monopoles 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 of the effective charge at a few soliton radii in this purely Coulombic system and compare it with the running of the coupling in perturbative QED.