# Hylomorphic Vortices in Abelian Gauge Theories - Mathematical Physics

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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- Maxwellequations, which provide models for the interaction between the electromagneticfield and matter. We assume that the nonlinear term is such that the energyfunctional is positive; this fact makes the theory more suitable for physicalmodels. A three dimensional vortex is a finite energy, stationary solution ofthese equations such that the matter field has nontrivial angular momen- tumand the magnetic field looks like the field created by a finite solenoid. Undersuitable assumptions, we prove the existence of three dimensionalvortex-solutions.

Author: ** Vieri Benci, Donato Fortunato**

Source: https://arxiv.org/