In this post we will cover the classic calculation of Bogomolny and obtain the energy bound. This bound is saturated in a very especial way leading to the linear Bogomolnyi equation, of great importance in the study of solitons. These equations hide a remarkable complex structure of solitons. Results on the dynamics of multivortex solutions are gouped in Taubes Theorem.

We give a brief discussion about domain wall junctures. This arise as a consecuence of the potencial of having more than two degenerate minima. We also treat the Bogomolny equations for this problem.

In this post I present my work on homotopy theory and its role in the classification of topological solitons in dimensions $d=1,2,3$. This work was the final assignment for approving the course on Mathematical Methods in Mathematical Physics at my university.

In this post we will treat the Principle of Symmetric Criticality. We will see that this principle is not universally valid. We will also illustrate some examples of application of the principle.

This will be the first in a series of post about concepts in geometry of gauge fields and properties of Yang-Mills equations based on the book of Sir Michael Atiyah, Geometry of Yang-Mills Fields.

This is the first in a series of post about certain topics of Topology.In this post we treat one of the biulding blocks of Mathematics, that it, Topological Spaces as well as introducing open subsets.