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Vertex corrections are taken into account in the Schwinger-Dyson equation forthe nucleon propagator in a relativistic field theory of fermions and mesons.The usual Hartree-Fock approximation for the nucleon propagator is known toproduce the appearance of complex (ghost) poles which violate basic theorems ofquantum field theory. In a theory with vector mesons there are vertexcorrections that produce a strongly damped vertex function in the ultraviolet.One set of such corrections is known as the Sudakov form factor in quantumelectrodynamics. When the Sudakov form factor generated by massive neutralvector mesons is included in the Hartree-Fock approximation to theSchwinger-Dyson equation for the nucleon propagator, the ghost poles disappearand consistency with basic requirements of quantum field theory is recovered.Comment: 18 page

Ghost poles in the nucleon propagator: Vertex corrections and form factors