Prediction of theSU(3)⊗SU(3)configuration mixing as a relativistic effect in the naive quark model

The harmonic-oscillator quark model of hadrons implies relativistic internal volocities for the quarks. If, consequently, we use a relativistic treatment of the quark spin (by replacing Pauli spinors with Dirac spinors), we obtain not only corrections to the "static SU(6)" results for the axial-vector matrix elements $\frac{G_A}{G_V} or G^{*}$ (as shown by Bogoliubov), but the whole $\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(3\right)\mathrm{}$ configuration mixing at $p_z=\infty$, in a semiquantitative manner. The mixing operator is just the product of the Wigner rotations of quark spins. For the low-lying ${\frac{1}{2}}^{+}$ octet, the dominant representations are (6, 3), ($3,\overline{3}$), and (8, 1), in agreement with the phenomenological analysis of Buccella, De Maria, and Lusignoli. The SU(6) classification of hadrons is preserved; at rest, the hadron wave function corresponds to an SU(6) group whose spin generators are the sum of the mean spin operators (of Foldy and Wouthuysen) of the quarks.