Pseudoclassical theories of Majorana, Weyl and Majorana--Weyl particles

TL;DR

This paper develops pseudoclassical models for Majorana, Weyl, and Majorana--Weyl particles in even-dimensional space-times, and explores their quantum descriptions and equivalences with field theoretical models in specific dimensions.

Contribution

It constructs pseudoclassical theories for these particles in arbitrary even dimensions and establishes their quantum and field theoretical equivalences in certain space-time dimensions.

Findings

Quantum descriptions match field theory in specific dimensions.

Neutral particles coincide with Majorana particles in certain dimensions.

Weyl and Majorana--Weyl particles are characterized in higher-dimensional space-times.

Abstract

A pseudoclassical theories of Majorana, Weyl and Majorana--Weyl particles in the space--time dimensions $D=2n$ are constructed. The canonical quantization of these theories is carried out and as a result we obtain the quantum mechanical description of neutral particle in $D=2n$ , Weyl particle in $D=2n$ and neutral Weyl particle in $D=4n+2$. In $D=2,4({\rm mod}8)$ dimensional space--time the description of the neutral particle coincides with the field theoretical description of the Majorana particle in the Foldy--Wouthuysen representation. In $D=8k+2$ dimensions the neutral Weyl particle coincides with the Majorana--Weyl particle in the Foldy--Wouthuysen representation.