How to remove diverges from the QED-Hartree approximation

The removal of divergences from the formal Hartree approximation of the vacuum charge density in quantum electrodynamics is discussed as a generalization of a procedure known from perturbative calculations in the Furry picture. A new diagrammatical justification of this procedure is given. Numerical tests are reported which show that the usual approach in the Furry picture can be modified to meet the requirements of approximations inspired by many-body theory. The calculations are based on the sum-over-modes expression of vacuum charge density-not in the usual version as spectral asymmetry, but in a formulation which takes into account corrections for the influence of the free Dirac sea. Owing to numerical expense, a self-consistent computation without further approximations in the sums over modes proves to be impracticable.