Relativistic scattering theory of charged spinless particles

In the context of a relativistic quantum mechanics we discuss the scattering of two and three charged spinless particles. The corresponding transition operators are shown to satisfy four-dimensional Lippmann-Schwinger and eight-dimensional Faddeev-type equations, respectively. A simplified model of two particles with Coulomb interaction can be solved exactly. We calculate: (i) The partial waveS-matrix from which we extract the bound state spectrum. The latter agrees with a fourth-order result of Schwinger, (ii) The full scattering amplitude which in the weakfield limit coincides with the expression derived by Fried et al. from eikonalized QED.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.Based on part of the Ph D. thesis by M. Hannemann, Mainz, 1985.