Partially conserved axial-vector current and the nonleptonic K-meson decays

Current commutation relations and a partially conserved axial-vector current hypothesis (PCAC) are applied to the nonleptonic K decays. On the assumption that the effective weak interactions should have the transformation property suggested by Gell-Mann in the quark model of the chiral symmetry, and that the axial-vector isospin charges to which the pions are related through PCAC should be generators of U(2)×U(2), the K2π and the K3π decay amplitudes, in which the four-momenta of all the final pions are continued to zero, are proved to obey the ΔI=1/2 rule. In the approximation of neglecting the continuation, the decay rate of the K3π is related to that of the K2π. The ratio of the decay rates is estimated and a reasonable agreement with experiment is obtained. Only the charge independence is assumed for the strong interactions.