Majorana and the Infinite Component Wave Equations

Abstract

I review the paper of Majorana about relativistic particles with arbitrary spin written in 1932. The main motivation for this papers was the dissatisfaction about the negative energy solutions of the Dirac equation. As such, the paper became immediately obsolete due to the almost contemporaneous discovery of the positron. However, for the first time, the unitary representations of the Lorentz group were introduced. Majorana considered two particular representations (named, after him, Majorana representations) which enjoy many interesting properties. A discussion about the reasons for its revival in the 60's is presented.