Salpeter's approach to the relativistic two-body problem

We apply Salpeter's approach to the calculation of relativistic two-body bound states. In addition to the intermediate propagation of two particles, Salpeter's approach allows for the propagation of two antiparticles As a consequence, Salpeter's equation becomes identical in structure to a random phse approxiamtion (RPA) equation familar from the study of nuclear collective excitations. Thus, for a sufficiently attractive interaction, Salpeter's equation might give rise to imaginary eigenvalues. The occurrence of imaginary eigenvalues is an indication of a pairing instability against the formation of strongly bound particle and antiparticle pairs. This pairing instability develops once the energy gap between two-particle and two-antiparticle states, originally at 4M, disappears. To illustrate Salpeter's approach, we calculate the relativistic two-body amplitude and bound state energy for the deuteron in Walecka's scalar-vector model