LOG#158. Ramanujan’s equation.

Hi, everyone! I am back, again! And I have some new toys in order to post faster (new powerful plugin). Topic today: Ramanujan! Why Ramanujan liked the next equation? (1)   This equation can be rewritten as follows (2)   … Continue reading

LOG#099. Group theory(XIX).

Final post of this series! The topics are the composition of different angular momenta and something called irreducible tensor operators (ITO). Imagine some system with two “components”, e.g., two non identical particles. The corresponding angular momentum operators are: The following … Continue reading

LOG#098. Group theory(XVIII).

This and my next blog post are going to be the final posts in this group theory series. I will be covering some applications of group theory in Quantum Mechanics. More advanced applications of group theory, extra group theory stuff … Continue reading

LOG#097. Group theory(XVII).

The case of Poincaré symmetry There is a important symmetry group in (relativistic, quantum) Physics. This is the Poincaré group! What is the Poincaré group definition? There are some different equivalent definitions: i) The Poincaré group is the isometry group … Continue reading

LOG#096. Group theory(XVI).

Given any physical system, we can perform certain “operations” or “transformations” with it. Some examples are well known: rotations, traslations, scale transformations, conformal transformations, Lorentz transformations,… The ultimate quest of physics is to find the most general “symmetry group” leaving … Continue reading

LOG#095. Group theory(XV).

The topic today in this group theory thread is “sixtors and representations of the Lorentz group”. Consider the group of proper orthochronous Lorentz transformations and the transformation law of the electromagnetic tensor . The components of this antisymmetric tensor can … Continue reading

LOG#094. Group theory(XIV).

Group theory and the issue of mass: Majorana fermions in 2D spacetime We have studied in the previous posts that a mass term is “forbidden” in the bivector/sixtor approach and the Dirac-like equation due to the gauge invariance. In fact, … Continue reading

LOG#093. Group theory(XIII).

The sixtor or 6D Riemann-Silberstein vector is a complex-valued quantity up to one multiplicative constant and it can be understood as a bivector field in Clifford algebras/geometric calculus/geometric algebra. But we are not going to go so far in this … Continue reading

LOG#091. Group theory(XI).

Today, we are going to talk about the Lie groups and , and their respective Lie algebras, generally denoted by and by the physics community. In addition to this, we will see some properties of the orthogonal groups in euclidena … Continue reading