Abstract
The asymptotic condition is stated in the case of a non-relativistic Coulombic potential (long-range interaction), and the corresponding LSZ reduction formula is established for the S-matrix elements of the theory. Since the Coulombic Green function is known in closed (non-perturbative) form, we are able to rigorously prove that the resulting S-matrix is free of infinite Coulombic phases and coincides with Dollard's S-matrix. A brief discussion of the forward-scattering amplitude is also given.
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