| The memory-function approach is applied to the relativistic two-particle problem. We thus obtain integral equations similar to the Bethe-Salpeter equation, taking all retardation effects fully into account and eliminating the relative time variable. The formalism is studied for scalar Klein-Gordon fields as well as for spinorial Dirac fields. For both cases the memory function and the integral kernels are calculated for a given model explicitly. The scalar-scalar model of Cutkosky is treated in detail and numerical binding energies are obtained, very close to those of the original Bethe-Salpeter equation, thus showing the extreme importance of retardation effects. As an example for Dirac fields the memory function for a proton-antiproton pair interacting via exchange of a $\pi^0$ is established. |
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