Broken Chiral Symmetry. III.SW(3)Theory and Soft-Pion Corrections

Starting with the $\mathrm{SW}\left(3\right)\mathrm{}$ group as the fundamental symmetry group, we develop a theory for the continuous breaking of this symmetry, in analogy with the theory based on the $W\left(3\right)\mathrm{}$ group discussed earlier. Despite what appears at first sight, there are considerable differences in the two theories, and in the present case one can avoid many difficulties associated with the $W\left(3\right)\mathrm{}$ theory. Several refinements of the arguments given earlier are also presented, which lead to mass formulas for $\pi$ and $K$ as well as the $\eta$ meson. A method to calculate finite-mass corrections to soft-pion theorems is also proposed and applied to a few problems.