Electrically charged localized structures

TL;DR

This paper explores localized electric charge structures within Abelian gauge fields coupled to scalar media, developing a first order solution framework and providing analytical examples with internal structure in various dimensions.

Contribution

It introduces a novel energy minimization method to obtain first order equations for localized charged structures in gauge-scalar systems.

Findings

Derived first order equations for localized charge solutions.

Provided analytical examples with internal structure.

Applied the method to models in 2D and 3D.

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.