Abstract
This work deals with an Abelian gauge field in the presence of an electric charge immersed in a medium controlled by neutral scalar fields, which interact with the gauge field through a generalized dielectric function. We develop an interesting procedure to solve the equations of motion, which is based on the minimization of the energy, leading us to a first order framework where minimum energy solutions of first order differential equations solve the equations of motion. We investigate two distinct models in two and three spatial dimensions and illustrate the general results with some examples of current interest, implementing a simple way to solve the problem with analytical solutions that engender internal structure.
Highlights
Localized finite energy structures play an important role in nonlinear science in general
We have studied the effects of a static electric charge immersed in a medium with generalized dielectric function
We implemented a first order framework, in which the equations of motion are solved by solutions of first order differential equations, which describe field configurations that minimize the energy of the localized structures
Summary
Localized finite energy structures play an important role in nonlinear science in general. Kinks can be immersed in the plane as domain ribbons and in space as domain walls, and vortices can behave as stringlike objects when immersed in the space These structures are well-known objects and have been studied in several distinct contexts in high energy physics, and in applications in several areas of nonlinear science. The use of a field-dependent function coupled with the gauge field dynamical term has been recently considered in [14] in the electric context, that is, in the presence of an electric charge fixed at the origin; there, we showed that the electric field has a behavior that captures the basic feature of asymptotic freedom, an effect that is usually associated to quarks and gluons It was considered, for instance, in [15,16,17,18,19] to describe vortex configurations with internal structures in the plane in the magnetic context. The field-dependent function can be used to modify the magnetic properties of the medium to study vortices, as in [7,8,9,15,16,17,18,19], but it can be considered to modify electrical properties of the medium, as in [3,4] and in [14], for instance
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