TL;DR
This paper develops a point particle approximation for well-separated vortices in the abelian Higgs model, deriving their interaction potential and modeling vortex scattering.
Contribution
It introduces a static point particle model for vortices, identifying their sources as scalar monopoles and magnetic dipoles, and computes their interaction potential.
Findings
The vortex source charges are numerically determined for various couplings.
The interaction potential is derived from the linearized field theory.
The model successfully describes type II vortex scattering.
Abstract
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 centre. 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.
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