  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).
