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We study the Dirac equation coupled to scalar and vector Klein-Gordon fieldsin the limit of strong coupling and large masses of the fields. We proveconvergence of the solutions to those of a cubic non-linear Dirac equation,given that the initial spinors coincide. This shows that in this parameterregime, which is relevant to the relativistic mean-field theory of nuclei, theretarded interaction is well approximated by an instantaneous, localself-interaction. We generalize this result to a many-body Dirac-Fock equationon the space of Hilbert-Schmidt operators.

The Dirac-Klein-Gordon system in the strong coupling limit