  Vertex corrections are taken into account in the Schwinger-Dyson equation for
the nucleon propagator in a relativistic field theory of fermions and mesons.
The usual Hartree-Fock approximation for the nucleon propagator is known to
produce the appearance of complex (ghost) poles which violate basic theorems of
quantum field theory. In a theory with vector mesons there are vertex
corrections that produce a strongly damped vertex function in the ultraviolet.
One set of such corrections is known as the Sudakov form factor in quantum
electrodynamics. When the Sudakov form factor generated by massive neutral
vector mesons is included in the Hartree-Fock approximation to the
Schwinger-Dyson equation for the nucleon propagator, the ghost poles disappear
and consistency with basic requirements of quantum field theory is recovered.
