Nuclear Physics A.563 (1993) 549-583 North-Holland NUCLEAR PHYSICS A The Bethe-Salpeter equation and the dispersion relation technique V.V. Anisovich zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Petersburg Nuclear Physics Institute, Gatchina, 188350 St. Petersburg, Russian Federation D.I. Melikhov Nuclear Safety Institute, Russian Academy of Sciences, Moscow, Russian Federation B.Ch. Metsch, H.R. Petry Institut fiir 7’heoretische Kernphysik, Universitiit Bonn, Bonn, Germany Received 7 April 1993 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Abstract We compare results for two-particle scattering amplitudes and for composite particle wave functions and form factors obtained in the framework of a dispersion relation approach with the corresponding solutions of the BS equation. 1. Introduction The development of a covariant technique is an important issue both for the description of composite particles and for scattering processes at low and interme- diate energies. Relativistic effects are important even for nuclei, the weakly bound systems of nucleons. They should play a crucial role in highly excited meson and baryon states considered as composite systems of quarks. Here we discuss the Bethe-Salpeter CBS) equation [ll, which is widely used for scattering processes and bound systems (see, for example, recent papers [2-41 and references therein), and compare it with a treatment of the same amplitudes based on a dispersion relation. The dispersion-relation method has some technical advantages which allow one to perform calculations in a comparatively simple form. For example, there are no problems with mass-of-shell amplitudes. So, it seems important to clarify the common points of these approaches as well as to stress the differences. We show that the dispersion-relation expression for the scattering amplitude may be obtained as a solution of the BS equation with separable interaction of the 03759474/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved