Algebra of Currents, Divergence of Strangeness-Changing Vector Currents, Unsubtracted Dispersion Relations, and theKl3form Factors

On the basis of current algebra, the Nambu-Sakurai hypothesis of partial conservation of strangeness-changing vector currents, and unsubtracted dispersion relations for $f_{+}\left(q^2\right)$ and $q^2{f}_{-}\left(q^2\right)$, the $K_{l3\mathrm{}}$ parameters $\xi$, ${\lambda }_{+}$, and ${\lambda }_{-}$ are found to be consistent with the present experimental indications. The only input in the theory is $\frac{F_K}{F_{\pi }{f}_{+}\mathrm{}\left(0\right)\mathrm{}}=1.28\mathrm{}$ from the Cabibbo theory. The mass of the conjectured $\kappa$ is in agreement with the recently reported result of broken chiral symmetry.