Continued-fraction representation of propagator functions in a Bethe-Salpeter model

Abstract

Using the well-known relation between the vertex function and the Bethe-Salpeter amplitude and knowledge of the bound-state energy eigenvalues of the Bethe-Salpeter equation, a continued fraction representation for the modified meson propagator D_F' is obtained. The Bethe-Salpeter equation for the nucleon-antinucleon problem with a massless-pseudoscalar-meson coupling is solved in a certain approximation, and the corresponding energy eigenvalues are determined through a continued-fraction technique. We have considered the nucleon both as a Dirac particle and also as a scalar particle. The analytic properties of the continued fraction are discussed and the existence of a Lehmann spectral-function representation for the D_F' obtained in the approximation is shown.