Equivalence of the Dirac Equation to a Subclass of Feynman Diagrams

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Abstract
The Dirac equation of an electron in a Coulomb field is shown to be equivalent to a certain subclass of Feynman diagrams taken within the eikonal approximation. The result is obtained via analysis of a two-body scattering amplitude, wherein the role of the heavier of the two particles involved is to generate the effective external potential in which the lighter particle propagates. The poles of the scattering amplitude are found to be the well-known relativistic binding energies.

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