Color and Isospin Waves from Tetrahedral Shubnikov Groups

TL;DR

This paper explores how internal spin waves, called mignons, within a discrete internal space governed by Shubnikov groups, can explain the spectrum of quarks and leptons, providing detailed mechanisms and explicit ground states.

Contribution

It introduces a detailed mechanism for internal spin waves (mignons) using Shubnikov groups to explain quark and lepton spectra, expanding on previous vibrational mode models.

Findings

Mignon mechanism explained in detail

Shubnikov group used to describe spectrum

Explicit mignetic ground state provided

Abstract

This note supplements a recent article in which it was pointed out that the observed spectrum of quarks and leptons can arise as quasi-particle excitations in a discrete internal space. The paper concentrated on internal vibrational modes and it was only noted in the end that internal spin waves ('mignons') might do the same job. Here it will be shown how the mignon-mechanism works in detail. In particular the Shubnikov group $A_4 + S (S_4 - A_4)$ will be used to describe the spectrum, and the mignetic ground state is explicitly given.