2008/09/26 by Marcu S. Cohen, Cohen, Marcu S.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.0809.4714
openalex publication_date 2008/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Spinors are lightlike. How do they combine to make massive particles? We visit the zoo of Lagrangian singularities, or caustics, in spacetime projections from spin space- the phase space of lightlike, 8- spinor flows. We find that the species living there are the elementary particles. Codimension J=(1,2,3,4) phase singularities - vortex lines, sheets, tubes, and knots, are classified by the Coxeter groups generated by multiplicity s reflections: "mass scatterings" off the vacuum spinors, that keep chiral pairs of matter envelopes confined to a timelike world tube, endowing a bispinor particle with mass. Using the volume in spin space as the action, the particle masses emerge in terms of the multiplicities, s: the number of null zigzags needed to close a cycle of mass scatterings. These mass values (calculated to lowest order in the vacuum intensity) are within a few percent of the observed masses for the leptons (J=1) and hadrons (J=3) ; but are up to 25 percent off for the mesons (J=2).