Kuo Transformation in Linear and Nonlinear Chiral-Symmetry Theories

Model Hamiltonians with (3, 3*) ⊕ (3*, 3)-violating interaction in the theory of Gell-Mann, Oakes, and Renner have been investigated for both cases of linear and nonlinear realizations of the $\mathrm{SW}\left(3\right)\mathrm{}$ theory in connection with the Kuo transformation. For the linear case, all mass formulas remain unchanged under the transformation, but not for the nonlinear case. Also, scattering amplitudes are found not to be invariant in general under the Kuo transformation for the nonlinear case. Physical interpretations of these puzzling facts are discussed in detail.