Composite systems viewed as relativistic quantal rotators: Vectorial and spinorial models

The constrained relativistic Hamiltonian dynamics of Dirac is applied to two models for composite objects having a nontrivial internal space. One model has a four-vector as internal manifold, the other a real four-spinor. The corresponding quantum mechanics is developed, and the two models each possess a Regge trajectory (mass related to spin) having the minimal ($2S+1$) degeneracy, unlike the Regge-Hanson spherical top model with ${\mathrm{}(2S+1)\mathrm{}}^2$ degeneracy. The spinorial model is most promising and allows (in the quantal case) electromagnetic interactions via minimal coupling, leading, for example, to intrinsic spin magnetic moments. An extension to "relativistic SU(6)" is shown to exist.