Majorana equation and its consequences in physics and philosophy

We focus here on the work of the italian physicist Ettore Majorana, and more particularly on his 1937 article on the symmetrical theory of the electron and the positron, probably one of the most important theory for contemporary thought. We recall the context of this article (Dirac relativistic electron wave equation) and analyze how Majorana deduces his own equation from a very general variational principle. After having rewritten Majorana equation in a more contemporary language, we study its implications in condensed matter physics and their possible applications in quantum computing. Finally, we describe some of the consequences of Majorana approach to philosophy.