The method of phenomenological nonlinear Lagrangians is described in detail for the case of chiral SU(2)×SU(2). The complete nonlinear Lagrangian is constructed for a theory of pions, nucleons, and vector and axial-vector mesons. The Lagrangian allows a study of the strong and weak interactions of the particles involved. Relations between masses and coupling constants emerge. A model containing only pions and nucleons is also described. Finally, the way to generalize the method to SU(3)×SU(3) is indicated.
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Wess et al. (1967) studied this question.
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