Hylomorphic Vortices in Abelian Gauge Theories

Details Hylomorphic Vortices in Abelian Gauge Theories Hylomorphic Vortices in Abelian Gauge Theories

2009-03-19

arxiv.org/abs/0903.3322v1

Physics

Mathematical Physics

Scientific paper

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.

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