A recollection of Souriau's derivation of the Weyl equation via geometric quantization

TL;DR

This paper revisits Souriau's work on geometric quantization of massless spin-1/2 particles, highlighting overlooked aspects and providing detailed explanations of his derivation of the Weyl equation.

Contribution

It clarifies and expands on Souriau's geometric quantization approach to derive the Weyl equation for massless particles, including missing details about Poincaré-invariant polarizers.

Findings

Rephrased and explained Souriau's sections on geometric quantization.

Provided missing details on the use of Poincaré-invariant polarizers.

Memorialized Souriau's contributions to the derivation of the Weyl equation.

Abstract

These notes merely intend to memorialize Souriau's overlooked achievements regarding geo\-metric quantization of Poincar\'e-elementary symplectic systems. Restricting attention to his model of massless, spin-$\half$, particles, we faithfully rephrase and expound here Sections (18.82)--(18.96) & (19.122)--(19.134) of his book \cite{SSD} edited in 1969. Missing details about the use of a preferred Poincar\'e-invariant polarizer are provided for completeness.