Induced Representations of Strong Coupling Groups

Abstract

Mackey's method of induced representations is applied to the strong coupling group G = K·T, where K is compact and T is Abelian, to obtain the general irreducible representations. The form of the meson‐isobar‐isobar couplings is obtained by reducing these, with the use of the Peter‐Weyl theorem, to irreducible representations of the compact subgroup K. The results are applied to the cases: pseudoscalar octet mesons, K = SU₂ ⊗ SU₃, T = T₂₄, and SU₆ 35‐plet mesons, K = SU₆, T = T₃₅. Explicit representations are obtained which are consistent with mass formulas $\mathcal{M}{\mathrm{\propto f}}_2\mathrm{(\mu )-}\frac{5}{8}\text{j(j+1)}$ and $\mathcal{M}{\mathrm{\propto G}}^2$ in the respective cases.