@MISC{Benci903contents, author = {Vieri Benci and Donato Fortunato}, title = {Contents}, year = {903} }

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Abstract

We consider an Abelian Gauge Theory in R 4 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 momentum 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.