SMatrix Approach to Internal Symmetries. II
Abstract
An Smatrix 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 Smatrix diagonalization postulate which corresponds to patterns of symmetry breaking is an Smatrix stationary principle. In a calculation retaining only firstorder deviations from the limit of exact symmetry, it is shown that crossing and unitarity determine what linear relations between Smatrix elements can remain stationary under a perturbation from the symmetry limit. Amplitude relations of conventional broken symmetries are thus derived for the breaking of isotopicspin 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.
 Publication:

Physical Review
 Pub Date:
 September 1968
 DOI:
 10.1103/PhysRev.173.1671
 Bibcode:
 1968PhRv..173.1671R