Massive Particles from Massless Spinors

TL;DR

This paper explores how massless spinors combine through spacetime caustics and phase singularities, resulting in elementary particles with masses derived from spin space volume and multiplicities, aligning closely with observed particle masses.

Contribution

It introduces a novel geometric framework linking spinor caustics and Coxeter group classifications to particle mass generation, providing a new perspective on mass emergence.

Findings

Mass values for leptons and hadrons closely match observed data.

Mass calculations are within a few percent for leptons and hadrons.

Meson mass estimates are up to 25 percent off from observed values.

Abstract

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).