SCHWINGER VARIATIONAL PRINCIPLE IN SCATTERING-THEORY

We give a detailed account on the application of the Schwinger variational principle (SchVP) for the evaluation of operator Pade approximates (OPA's). OPA's can be considered in their simplest ''one-loop'' (ladder) form as solutions of scattering equations but allow for a more natural transition to quantum field theory beyond ladder approximation. Therefore methods for their evaluation are of high interest. One of these methods is the SchVP which we study in the special case of elastic nucleon-nucleon scattering in terms of the Blankenbecler-Sugar equation. Since exact proofs of convergence for the SchVP cannot be found in general, the intention of our paper is to give by a detailed study of this complex example a justification for the application of the SchVP in even more complex situations. Applying the SchVP, it is shown that relatively simple and quite precise approximations for the T-matrix elements can be constructed valid for the whole energy range under consideration.