Ponicaré group,V−A, and SU(3) as spectrum-generating group in leptonic decays

From as few assumptions as possible about the relations among the Poincaré group, the particle-classifying SU(3), and $V-A$ we derive properties of the $K_{l3\mathrm{}}$ and $K_{l2\mathrm{}}$ decays. From the assumed relation between SU(3) and the Poincaré group and the first-class condition it follows that the form-factor ratio $\xi$ of $K_{l3\mathrm{}}$ decay is $\xi =-0.57\mathrm{}$, and that a value of $\xi =0\mathrm{}$ is in disagreement with very general and well-accepted theoretical assumptions. Assuming universality of $V-A$, the Cabibbo suppression is derived from the relations between SU(3) and $V-A$ as a consequence of the brokenness of SU(3).