Massive Particles from Massless Spinors
  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). 
Marcu S. Cohen