Spin Singularities: Clifford Kaleidoscopes and Particle Masses

TL;DR

This paper explores the idea that elementary particles are singularities in a complex phase space, with their properties like mass and charge arising from the geometry and topology of these singularities, aligning with observed particle families.

Contribution

It introduces a novel classification of particle-like singularities using Clifford Kaleidoscopes and Coxeter groups, linking their geometric properties to particle masses and quantum numbers.

Findings

Singularities classified by Coxeter groups match particle families.

Quantized masses of singularities closely align with observed particle masses.

Phase-space singularities exhibit properties consistent with leptons, mesons, and hadrons.

Abstract

Are particles singularities- vortex lines, tubes, or sheets in some global ocean of dark energy? We visit the zoo of Lagrangian singularities, or caustics in a spin(4,C) phase flow over compactifed Minkowsky space, and find that their varieties and energies parallel the families and masses of the elementary particles. Singularities are classified by tensor products of J Coxeter groups <p,q,r>s generated by reflections. The multiplicity, s, is the number reflections needed to close a cycle of null zigzags: nonlinear resonances of J chiral pairs of lightlike matter spinors with (4-J) Clifford mirrors: dyads in the remaining unperturbed vacuum pairs. Using singular perturbations to "peel" phase-space singularities by orders in the vacuum intensity, we find that singular varieties with quantized mass, charge, and spin parallel the families of leptons (J=1), mesons (J=2), and hadrons (J=3). Taking the symplectic 4 form - the volume element in the 8- spinor phase space- as a natural Lagrangian, these singularities turn out to have rest energies within a few percent of the observed particle masses.