Abstract
Using the [current, charge] equal-time commutation relations and the hypothesis of partially conserved axial-vector current, we have obtained a number of sum rules between off-mass-shell matrix elements for the high-energy neutrino-nucleon "inelastic" processes. In addition, the $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ chiral algebra has enabled us to express the pion-production matrix element in terms of $\ensuremath{\beta}$-decay form factors in a most straightforward manner. The results obtained are in reasonable agreement with the experimental data available and the previous models.
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