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Three-dimensional vortices in Abelian gauge theories. (English) Zbl 1173.81013

The theory of Abelian gauge theories in \(\mathbb{R}^4\) equipped with the Minkowski metric leads to a system of KGM (Klein-Gordon-Maxwell) equations, which provide models for the interaction between the electromagnetic field and matter. The authors show that a suitable choice of the term \(W\) guarantees the existence of finite energy vortices in tree space dimensions. Here, a vortex is a finite energy solution in which the magnetic field looks like the field created by a solenoid.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
51B20 Minkowski geometries in nonlinear incidence geometry
47J30 Variational methods involving nonlinear operators
35J50 Variational methods for elliptic systems
81V10 Electromagnetic interaction; quantum electrodynamics
35Q60 PDEs in connection with optics and electromagnetic theory
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