# Tag: physics

- Vortices: Bogomol'ny equations and Taubes Theorem (20 May 2021)

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. - Solitons: Vortices in the Ginzburg-Landau Theory - the gauged theory case (15 May 2021)

In this post we will cover the vortex solutions in the gauged Ginzburg-Landau theory. - Solitons: Vortices in the Ginzburg-Landau Theory - the global theory case (29 Apr 2021)

In this post we will cover the vortex solutions in the Ginzburg-Landau theory. We will focus on the global theory only. - Solitons: Generalizations of the kink (02 Apr 2021)

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. - Solitons: Sine-Gordon kink (16 Mar 2021)

In this post we talk about the Sine-Gordon kink solution. We discuss the Bogomolnyi bound for this case and its non linear realization. - Solitons: The kink (11 Mar 2021)

In this post we talk about the most basic soliton, the kink. We review some of its properties and the conserved topological charge. - The Reeh-Schlieder Theorem and vacuum entanglement (26 Feb 2021)

In this post I present my final assignment for the elective course Seminar on Quantum Mechanics and Information Theory. - Homotopy Theory and Classification of Topological Solitons (12 Feb 2021)

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. - The field equations for a Gauge Theory (05 Feb 2021)

This second post will be about the field equations for a gauge theory. This is a direct generalization of Maxwell's equations. - The principle of symmetric criticality (02 Feb 2021)

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. - The geometry of Gauge Fields (20 Dec 2020)

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. - The ALPHA experiment at CERN (19 Jul 2020)

We review how to find the solution for the electromagnetic four-potential in the Lorentz gauge. - Covariant solution of Maxwell Equations (29 Jun 2020)

We review how to find the solution for the electromagnetic four-potential in the Lorentz gauge. - Clifford Algebra and SO(2n) representations (08 Apr 2020)

In this post I review Spinor representations of SO(2n). Also, we treat Clifford algebra generators and its connection with orthogonal groups.