Hylomorphic Vortices in Abelian Gauge Theories

TL;DR

This paper proves the existence of finite energy, three-dimensional vortex solutions in an Abelian gauge theory modeled by Klein-Gordon-Maxwell equations, representing stable electromagnetic-matter interactions with nontrivial angular momentum.

Contribution

It introduces the first rigorous proof of 3D vortex solutions in Abelian gauge theories with positive energy functionals, expanding understanding of such models in physics.

Findings

Existence of finite energy vortex solutions

Vortices have nontrivial angular momentum

Magnetic field resembles that of a finite solenoid

Abstract

We consider an Abelian Gauge Theory in R4 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. We assume that the nonlinear term is such that the energy functional is positive; this fact makes the theory more suitable for physical models. A three dimensional vortex is a finite energy, stationary solution of these equations such that the matter field has nontrivial angular momen- tum and the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of three dimensional vortex-solutions.