Math Stuff

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Tag: math

  • 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.
  • 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 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.
  • Integration of p-forms over p-chains (23 Nov 2020)
    Finally, we give introduce the concept of integration of p-forms over p-chains.
  • Introduction to r-simplexes and r-chains (19 Nov 2020)
    We give an introduction to r-simplexes and r-chains in order to introduce the notion of integration over r-chains.
  • Closed Subsets and Bases for a Topology (17 Jun 2020)
    In this second post about topology we introduce the concept of closed subsets and bases for a topology.
  • Topological Spaces (15 May 2020)
    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.
  • 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.