Nonlinear Hadron Couplings from Divergence Conditions. I. Pions and Nucleons

It is shown that chiral-dynamical models for the pion-nucleon system can be obtained simply by requiring that the source function in the pion field equation be expressible as a complete divergence. Both nonderivative and derivative pion-nucleon couplings are considered. The nonderivative-coupling case yields models with one coupling constant, while the derivative-coupling case leads to models involving two coupling constants. Since our approach avoids the use of chiral symmetry, it does not raise the problems associated with a broken symmetry. It is also suggested that the nonlinear pion-nucleon coupling, arising from the divergence condition, might very well represent a fundamental coupling rather than merely an effective coupling.