Reggeization of Quark Number

In earlier work the Reggeization of approximate dynamical groups has been presented as a calculational method for classifying particles and evaluating $S$-matrix elements at high energies. In continuation of this work, an especially simple model is considered where just one invariant of the higher $U\left(6\right)\mathrm{}\times U\left(6\right)\mathrm{}$ approximate symmetry, quark-plus-antiquark number, is Reggeized. The resulting classification of particles (according to their quark content) into exploding supermultiplets of spin and unitary spin, and the formulas for computing $S$-matrix elements, are given for high energies, where an exchange of an $N$-plane trajectory in the cross channel may be expected to dominate the scattering. The hope is that this analysis may help reduce the large number of parameters now used in Regge theory by combining Regge ideas with higher symmetries. The type of Fourier expansion on a higher approximate symmetry group and the Regge technique used here for evaluating asymptotic behavior may possess wider applications than the case considered in this paper.