Three-dimensional vortices in Abelian gauge theories

In this paper we consider an Abelian Gauge Theory in R4R4 equipped with the Minkowski metric. This theory leads to a system of equations, the Klein–Gordon–Maxwell equations, which provide models for the interaction between the electromagnetic field and matter. A three-dimensional vortex is a finite energy solution of these equations in which the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of vortex solutions.