Weak-Coupling Currents and Symmetries of Strong Interactions

The general isotopic properties of bilinear currents which will lead to the $\left|\Delta S\right|\le 1$ and $\left|\Delta I\right|=\frac{1}{2}$ rules for weak decay processes are examined. The latter rule is re-expressed in terms of an equivalent mathematical statement which permits one to obtain the usual predictions in a simple manner. In general, when the strangeness-conserving part of such a current is an isotopic vector, the strangeness-changing part can be a linear combination of $I=\frac{1}{2}$ and $I=\frac{3}{2}$ currents. The existence of an $I=\frac{3}{2}$ current could be established by experiments on the decays $K\to \pi +\mathrm{leptons}$, or on high-energy neutrino capture, $\nu +N\to \mu +\Sigma$. Experiments on $K_{e4\mathrm{}}$ decays could test the bilinearity of the current.