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