The Wick transformation in momentum space is modified to include all scattering energies by use of a coordinate surface which possesses limited detours into the complex relative energy plane. This device retains the simple form of the equation for the Bethe-Salpeter amplitude 4(&p,). It is shown that the transformation is valid if $(zp,) has the cut structure indicated by field theory, and this structure is shown to be consistent with the Bethe-Salpeter equation provided the interaction V (x) satisfies a simple causality condition. It is further shownthat the cut structure of a solu-tion to the transformedequation canbe deduced from the causal structure of the interaction alone without reference to field theory. Basic properties of the transformed equation are derived and a numerical treatment for purely elastic scattering is presented. (To be submitted to Journal of Math. Physics
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