Majorana and the Infinite Component Wave Equations

TL;DR

This paper reviews Majorana's 1932 work on relativistic particles with arbitrary spin, highlighting its historical context, the introduction of Lorentz group representations, and its subsequent influence and revival in physics.

Contribution

It presents a detailed analysis of Majorana's early work on infinite component wave equations and the properties of Majorana representations of the Lorentz group.

Findings

Introduction of unitary Lorentz group representations

Identification of Majorana representations with unique properties

Historical discussion on the revival of these ideas in the 1960s

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.