Solutions of the relativistic wave equation for three different coupling schemes to an external source are examined. The Regge trajectories are observed to exhibit a high degree of model dependence and to possess singularities which are often assumed absent in a fully relativistic theory. It is shown that these arise from multiple poles in the scattering amplitude and can occur in theories for which no collapse into the center is possible for physical values of the angular momentum.

• Received 21 November 1962

DOI:https://doi.org/10.1103/PhysRev.130.1259