Jost-Function Description for the Bethe-Salpeter Equation

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Abstract
A new formulation of the Bethe-Salpeter eigenvalue problem is presented. An integral representation of the eigenvalue condition is given which is a generalization of the familiar Jost function in nonrelativistic theory. The formalism is worked out in detail for the scalar-exchange potential and is used to examine Regge trajectories in the weak coupling limit. The detailed multiplicity of the lower trajectories is shown to depend on the behavior of the potential at the origin in coordinate space, and hence to be very potential-dependent.