Current Algebras and Meson Systems

We apply the algebra of compact $U\left(6\right)\mathrm{}\times U\left(6\right)\mathrm{}$, obtained from integrated current components, to meson systems. If we limit the sums over intermediate states to the lowest lying 36 $\mathrm{SU}\left(3\right)\mathrm{}$-invariant pseudoscalar and vector meson physical states at rest, then we obtain several of the predictions of $\mathrm{SU}\left(6\right)\mathrm{}$ models. On considering the commutation rules of magnetic-moment operators we obtain additional relations. Among these are $〈{r_{\pi }}^2〉=〈{r_{\rho }}^2〉$ and ${{\mu }_{\rho }}^2=\frac{1}{6}〈{r_{\rho }}^2〉$ relating the electric charge radii to the $\rho$-meson magnetic moment, with a pole model giving 2 magnetons for the $\rho$-meson total magnetic moment. We also find $\frac{〈{r_{\pi }}^2〉}{6}\simeq \frac{1.6}{{M_V}^2}$, using an additional consistency relation, in rough agreement with the vector-meson pole model. However, the radius of electric charge form factors is predicted to be the same as that of the divergence of the axial-vector current form factors, which disagrees with our present ideas about these form factors.