The nonlinear terms (shifting π) on the right-hand side of the second equation underlie the nonlinear realization of SO(4). The chiral group SU ( 2 ) L × × SU ( 2 ) R ≃ ≃ SO ( 4 ) is realized nonlinearly on the triplet of pions— which, however, still transform linearly under isospin SU ( 2 ) V ≃ ≃ SO ( 3 ) rotations parametrized through the angles { θ θ V } . By contrast, the { θ θ A } represent the nonlinear "shifts" (spontaneous breaking).