Relativistic Lippmann - Schwinger equation

The classical Lippmann-Schwinger equation plays an important role in the scattering theory (non-relativistic case, Schr"odinger equation). In the present paper we consider the relativistic analogue of the Lippmann-Schwinger equation. We represent the corresponding equation in the integral form. Using this integral equation we investigate the stationary scattering problems (relativistic case, Dirac equation). We consider the dynamical scattering problems (relativistic case, Dirac equation) as well.