Hylomorphic Vortices in Abelian Gauge Theories

Publication date: 19 March 2009

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.

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Variational methods for elliptic systems (35J50) Electromagnetic interaction; quantum electrodynamics (81V10)

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