Singularities of a Bethe-Salpeter Amplitude

The Bethe-Salpeter equation for the scattering of two particles of unequal mass is reduced to separable form by the use of the bipolar transformation. Exact solutions are obtained for Wick's kernel, so that the $S$ matrix and the Regge trajectories are explicitly determined. The daughter trajectories are identified for this kernel and are found to be related in the expected way with one another. It is shown that they make no contribution to the scattering amplitude on the mass shell. Trajectories are found corresponding to the abnormal solutions of Wick's equation, but these do not appear in the normal scattering amplitude.