Pseudoclassical theory of Mayorana--Weyl particle

TL;DR

This paper develops a pseudoclassical framework for Weyl particles in even-dimensional space-time, performs canonical quantization, and explores connections to Majorana-Weyl particles in quantum field theory, especially in 10 dimensions.

Contribution

It introduces a pseudoclassical model for Weyl particles in even dimensions and links it to quantum field theory descriptions of Majorana-Weyl particles.

Findings

Canonical quantization yields a Weyl particle theory in Foldy-Wouthuysen form.

Proposes a quantum mechanics framework for neutral Weyl particles in even dimensions.

Discusses the relation between pseudoclassical models and Majorana-Weyl particles in D=10.

Abstract

A pseudoclassical theory of Weyl particle in the space--time dimensions $D=2n$ is constructed. The canonical quantization of that pseudoclassical theory is carried out and it results in the theory of the $D=2n$ dimensional Weyl particle in the Foldy--Wouthuysen representation. A quantum mechanics of the neutral Weyl particle in even--dimensional space--time is suggested and the connection of this theory with the theory of Mayorana--Weyl particle in QFT is discussed for D=10.