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

Christian Duval (1, 2)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 7332

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.

Mots clés: Geometric Quantization; Weyl Equation

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]

Christian Duval. A recollection of Souriau's derivation of the Weyl equation via geometric quantization. 2016. ⟨hal-01266487⟩