S-matrix approach to internal symmetries. II

Abstract

An S-matrix formulation of internal symmetries reported in a previous paper is extended to the case of broken symmetries. It was shown before that crossing and unitarity can determine permitted internal symmetries by determining what constant real orthogonal matrices can diagonalize an S matrix. It is shown here that a generalization of the S-matrix diagonalization postulate which corresponds to patterns of symmetry breaking is an S-matrix stationary principle. In a calculation retaining only first-order deviations from the limit of exact symmetry, it is shown that crossing and unitarity determine what linear relations between S-matrix elements can remain stationary under a perturbation from the symmetry limit. Amplitude relations of conventional broken symmetries are thus derived for the breaking of isotopic-spin symmetry and unitary symmetry in the scattering of pseudoscalar mesons from pseudoscalar mesons. The application of unitarity on these amplitude relations leads to elegant derivations of mass formulas.