Rotator Model of Elementary Particles Considered as Relativistic Extended Structures in Minkowski Space

The purpose of this paper is to investigate some consequences of the assumption that elementary particles are not pointlike, but are rather, extended structures in Minkowski space.

In terms of the hypothesis that the internal quantum states of such structures correspond to internal "rotator" levels belonging to the Hilbert space containing all irreducible finite-dimensional representations of the group $S{O_3}^{*}$ of three-dimensional complex rotations (isomorphic to the Lorentz group), we obtain a particle classification which recovers (including leptons) the Nishijima-Gell-Mann classification of elementary particles. In this way, we justify the empirical Nishijima-Gell-Mann relation between isobaric spin, strangeness, baryon number, and charge. Moreover, as will be shown in a second paper, the new internal ("hidden") degrees of freedom which correspond to isobaric spin, strangeness, and baryon number open up new possibilities for understanding qualitatively and quantitatively the elementary particle interactions and decays; while a simple extension of "fusion" theory yields possible external state vectors and equations associated with any given internal quantized states corresponding to known elementary particles.