Color and Isospin Waves from Tetrahedral Shubnikov Groups

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.