Revisiting the Majorana Relativistic Theory of Particles with Arbitrary Spin

TL;DR

This paper revisits Majorana's relativistic theory, emphasizing its pioneering role in allowing particles of arbitrary spin and introducing a universal quantum equation that predates modern particle physics.

Contribution

It provides a detailed analysis and explicit formulation of Majorana's theory, including the construction of infinite matrices for wave functions of particles with arbitrary spin.

Findings

Majorana's theory predates modern concepts of arbitrary spin particles.

Explicit methods for constructing infinite matrices are presented.

The theory offers a universal framework for particles of any nature and speed.

Abstract

In 1932 Ettore Majorana published an article proving that relativity allows any value for the spin of a quantum particle and that there is no privilege for the half integer spin. The Majorana idea was so innovative for the time that the scientific community understood its importance only towards the end of the thirties. This paper aims to highlight the depth of the scientific thought of Majorana that, well in advance of its time, opened the way for modern particle physics and introduced for the first time the idea of a universal quantum equation, able to explain the behavior of particles with arbitrary spin and of any nature, regardless the value of their speed. It will be analyzed in detail and made explicit all the steps that lead to the physical mathematical formulation of the Majorana theory. A part of these steps require basic knowledge of quantum physics but not for this should be regarded as trivial since they show the physical meaning hidden into the structure of the equation. Moreover, the explicit method for the construction of the infinite matrices will be given, by which the infinite components of the wave functions representing the fundamental and excited states of the particle are calculated.