April 21, 2023
A one-pager about Mean field theory
What the title says.
Physics, Maths, Languages and a little History.
April 21, 2023
A one-pager about Mean field theory
What the title says.
May 20, 2021
Vortices: Bogomol'ny equations and Taubes Theorem
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.
May 15, 2021
Solitons: Vortices in the Ginzburg-Landau Theory - the gauged theory case
In this post we will cover the vortex solutions in the gauged Ginzburg-Landau theory.
May 01, 2021
The aulos: An Ancient Greek wind instrument
In this post we talk about an ancient greek wind instrument called aulos and introduce one of the best history pages on the web.
April 29, 2021
Solitons: Vortices in the Ginzburg-Landau Theory - the global theory case
In this post we will cover the vortex solutions in the Ginzburg-Landau theory. We will focus on the global theory only.
April 02, 2021
Solitons: Generalizations of the kink
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.
March 16, 2021
Solitons: Sine-Gordon kink
In this post we talk about the Sine-Gordon kink solution. We discuss the Bogomolnyi bound for this case and its non linear realization.
March 13, 2021
An introduction to Ancient Greek: The Greek Alphabet and Pronunciation Part 2
This is part two of the previous post on the greek alphabet and pronunciation.
March 11, 2021
Solitons: The kink
In this post we talk about the most basic soliton, the kink. We review some of its properties and the conserved topological charge.
March 09, 2021
An introduction to Ancient Greek: The Greek Alphabet and Pronunciation Part 1
Finally I pick the courage to start this journey of learning Ancient Greek. In this post we will learn the Greek alphabet and pronunciation.
February 26, 2021
The Reeh-Schlieder Theorem and vacuum entanglement
In this post I present my final assignment for the elective course Seminar on Quantum Mechanics and Information Theory.
February 12, 2021
Homotopy Theory and Classification of Topological Solitons
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.
February 05, 2021
The field equations for a Gauge Theory
This second post will be about the field equations for a gauge theory. This is a direct generalization of Maxwell's equations.
February 02, 2021
The principle of symmetric criticality
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.
December 20, 2020
The geometry of Gauge Fields
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.
November 23, 2020
Integration of p-forms over p-chains
Finally, we give introduce the concept of integration of p-forms over p-chains.
November 19, 2020
Introduction to r-simplexes and r-chains
We give an introduction to r-simplexes and r-chains in order to introduce the notion of integration over r-chains.
July 19, 2020
The ALPHA experiment at CERN
We review how to find the solution for the electromagnetic four-potential in the Lorentz gauge.
June 29, 2020
Covariant solution of Maxwell Equations
We review how to find the solution for the electromagnetic four-potential in the Lorentz gauge.
June 17, 2020
Closed Subsets and Bases for a Topology
In this second post about topology we introduce the concept of closed subsets and bases for a topology.
May 19, 2020
Early Monarchy and The Unification
This is a short text about the firsts pharaos of Egypt and how the unification happened.
May 15, 2020
Topological Spaces
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.
April 10, 2020
Packaging Python Projects
In this blogpost I explain how to create and upload a package to Python Package Index.
April 08, 2020
Clifford Algebra and SO(2n) representations
In this post I review Spinor representations of SO(2n). Also, we treat Clifford algebra generators and its connection with orthogonal groups.
April 07, 2020
How to Install Git on Windows
En este post voy a detallar como instalar Git en Windows .