Abstract
We deal with the presence of magnetic monopoles in a non Abelian model that generalizes the standard 't~Hooft-Polyakov model in three spatial dimensions. We investigate the energy density of the static and spherically symmetric solutions to find first order differential equations that solve the equations of motion. The system is further studied and two distinct classes of solutions are obtained, one that can also be described by analytical solutions which is called small monopole, since it is significantly smaller than the standard 't~Hooft-Polyakov monopole. The other type of structure is the hollow monopole, since the energy density is endowed with a hole at its core. The hollow monopole can be smaller or larger than the standard monopole, depending on the value of the parameter that controls the magnetic permeability of the model.
Highlights
In classical field theory, topological structures usually emerge as static solutions of the equations of motion that describe the system
III we present some distinct models for magnetic monopoles, one that admits new analytical solutions that engender a nonstandard profile, which we call the small monopole, and others that present solutions with energy density with a hole in its core, which we call hollow monopoles
Despite the presence of spherical symmetry, the equations of motion are coupled to second order differential equations and are hard to solve
Summary
Topological structures usually emerge as static solutions of the equations of motion that describe the system. Among the most known topological structures that appear in field theory are the kinks, vortices, and magnetic monopoles They are one-, two-, and threedimensional objects, respectively, and find several applications in high energy physics, to describe phase transitions and other features, and in condensed matter, where they may be used to describe specific properties of superconductors and magnetic materials; see, e.g., Refs. [10] we have studied vortices in a model where the Uð1Þ symmetry is enlarged to become Uð1Þ × Z2, with the magnetic permeability modified and controlled by an additional neutral scalar field that acts as a source field This modification gave rise to interesting solutions of vortices with internal structure.
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