Die darstellungen der starken kopplung und das resonanzproblem der meson-nucleon-streuung

Abstract

This paper deals with the completion of the strong-coupling method in meson field theory. By means of a canonical and non-linear transformation of variables the original meson field is split into a free meson part and a self field part of the nucleon. The transformation is defined so that the interaction between the compound nucleon system thus arising and the free mesons vanishes in the case of infinitely strong coupling. It is shown that there exists a family of transformations satisfying the conditions. A system of equations for certain transformation functions is stated as the consequence of the conditions. The solutions of the field-splitting problem are investigated. The general scheme for a strong-coupling approximation method based on this field splitting is derived, and the problem of calculating the pion-nucleon resonance scattering from the strong coupling theory is treated on this basis. A special approximation is made for calculations near the resonance. Numerical results obtained from such a calculation are discussed. For the sake of simplicity the symmetric scalar fixed-source meson theory is used. But the principle of the method will be the same in the more essential but more complicated symmetric pseudoscalar case. Thus the present considerations will serve to guide an analogous investigation using the symmetric pseudoscalar theory.