自旋奇点：Clifford万花筒和粒子质量
Spin Singularities: Clifford Kaleidoscopes and Particle Masses
摘要：
粒子是奇点--在全球暗能量海洋中的涡旋线、管道或片吗？我们参观了拉格朗日奇点的动物园，或者说是紧闵可夫斯基空间中自旋（4，C）相流中的焦散线，发现它们的种类和能量与基本粒子的族和质量平行。奇异性通过反射产生的J Coxeter群<p，q，r>s的张量积来分类。多重性s是闭合一个零旋量循环所需的反射次数：类光物质旋量的J手征对与（4-J）克利福德镜的非线性共振：剩余未微扰真空对中的对偶。使用奇异微扰“剥离”相空间奇异的真空强度的订单，我们发现，量子化的质量，电荷和自旋的奇异品种平行的轻子（J=1），介子（J=2）和强子（J=3）的家庭。以辛4形式--8旋量相空间中的体积元--作为自然拉格朗日量，这些奇点的静止能量在观测到的粒子质量的百分之几以内。
英文摘要：
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.
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