Green's Funtion Approach and Its Equivalence with the Ordinary N/D Method

Abstract

Green's function approach to the scattering of two particles in a channel with a one-particle intermediate state is investigated in detail under the elastic approximation, with due attention to propagator zeros. In relation to the asymptotic behavior of the spectral function in the Lehmann representation of the propagator, particles are classified into four types; super-elementary, elementary, intermediate and composite. It is shown that the present approach is equivalent to the ordinary N/D method. Criticism to some earlier works is also given.