SU4Mass Formula and Particle Classification Schemes

The mathematical derivation of the general mass formula of $S{U}_4$ is given. The derivation is preceded by a survey of the mathematical aspects of the group $S{U}_4$ and its representations. The possible elementary-particle symmetry schemes based on the Lie algebra of S${\mathrm{U}}_4$, most of which have already been proposed, are classified and systematically discussed. The extension of $S{U}_4$ to $S{U}_8$ by inclusion of ordinary spin is discussed and shown to rule out two of the three classes of models. Finally, a simple $S{U}_8$ model is sketched.