Derivation of the external field in the Dirac equation based on quantum electrodynamics

The multiphoton exchange between two charged spin [Formula: see text] particles of light (m) and heavy (M) mass is considered and it is shown how, in the limit M → ∞, the Dirac equation with an external potential including radiative corrections emerges. This result can only be achieved if diagrams with photons attached to the heavy particle line cancel among themselves for M → ∞. We have shown this in the lowest order where the individual diagrams have nonvanishing limits.