Abstract
The vertex function of an s-wave bound state in potential theory is discussed in terms of a non-relativistic Bethe-Salpeter formalism. It is shown that the Born series defining the off-shell amplitude, Γ(k2, P0), has the property that Γ(k2, k2/m)=Γ0/D(k2,λ), where D(k2, λ) is the Jost function for potential strength λ, and where the bare (Γ0) and physical (Γc) couplings are related by Γ0 = ΓcZ1, with Z1, the vertex renormalization constant equal to D(−α2, λ). The particular proof presented derives from a detailed comparison in momentum space of alternative, but equivalent, coordinate space definitions of the Jost function originating with Jost and Pais.
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