Majorana equation and its consequences in physics and philosophy

TL;DR

This paper examines Majorana's 1937 symmetric electron-positron theory, its derivation from variational principles, and explores its implications in condensed matter physics, quantum computing, and philosophy.

Contribution

It provides a contemporary reinterpretation of Majorana's equation and analyzes its interdisciplinary impacts in physics and philosophy.

Findings

Majorana's equation offers new insights into particle symmetry.

Implications for condensed matter physics and quantum computing.

Philosophical consequences of Majorana's approach are discussed.

Abstract

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.