Static intervortex forces

A point particle approximation to the classical dynamics of well-separated vortices of the Abelian Higgs model is developed. A static vortex is asymptotically identical to a solution of the linearized field theory (a Klein-Gordon-Proca theory) in the presence of a singular point source at the vortex center. It is shown that this source is a composite scalar monopole and magnetic dipole, and the respective charges are determined numerically for various values of the coupling constant. The interaction potential of two well-separated vortices is computed by calculating the interaction Lagrangian of two such point sources in the linear theory. The potential is used to model type II vortex scattering.