Nonlinear Lagrangian Transformations

In nonlinear Lagrangian schemes it is useful to transform the nonderivative pion-nucleon coupling into the derivative coupling. The effect of such a transformation on renormalization constants and closed-loop diagrams is investigated by direct calculations of the second-order nucleon and pion self-energies and the fourth-order nucleon-nucleon interaction with the inclusion of the renormalization diagrams. By carefully combining the contributions of appropriate diagrams, the complete equivalence of the nonderivative and derivative couplings is demonstrated.