Wednesday, May 10, 2017


Analytic solutions to coherent control of the Dirac equation and beyond  

My latest arxiv paper is online 

This work introduces Relativistic Dynamical Inversion (RDI) as a technique to find analytic solutions to the Dirac equation. 


Thursday, March 30, 2017

A course on Relativity using Clifford (geometric) algebras in Mathematica

I am posting my lectures notes on Classical and Quantum Relativistic Mechanics at

I am preparing these notes in Mathematica, so, there are actual functions that perform symbolic and numerical calculations. If you do not have Mathematica, you can download the companion pdf documents or download the Mathematica CFD player for free at:

These lecture notes employ the language of Clifford algebras in two flavors: The Algebra of the Physical Space (APS) and the  Space Time Algebra (STA).

Contrary to the literature about Clifford algebras in physics, I decided to heavily rely on matrix representations. Clifford algebras can be developed from elegant axiomatic principles where no matrix is necessary at all. Nevertheless, I personally saw that most people claim to be too busy for that. My hope is that a direct exposure of the matrix representation will give them a more familiar environment based on simple standard linear algebra. 

Two snapshots of randoms pages