Unsubtracted Dispersion Relations in Weak Interactions and Unitary Symmetry

Abstract

In a series of papers a dynamical approach to weak interactions based on unsubtracted dispersion relations has been introduced and discussed. Emphasis has been placed on the possible existence of eigenvalue restrictions arising from the homogeneity of the basic equations for the weak-interaction amplitudes, and the selection rules resulting from the eigenvalue restrictions have been derived when strong interactions possess certain symmetries. The following topics are covered in this paper: the irreducibility theorem for the weak-interaction amplitudes, generalization of the Goldberger-Treiman relation, derivation of the Gell-Mann-Okubo and Coleman-Glashow mass formulas from weak interactions as eigenvalue restrictions or self-consistency conditions, and a new approach to nonleptonic decays based on the empirical solution of the leptonic decays. Comparison of the theory of nonleptonic decays with experiments indicates that the agreement is satisfactory.