Vacuum-polarization potential, finite-size effects, and the coulomb propagator

A momentum representation for the fermion propagator in an external electromagnetic field is derived from which a convenient form for the vacuum-polarization potential is obtained. This expression, for which the trace has already been taken, can be used for calculating the dependence of higher-order corrections on the form factors of the external field. Expanding in powers of the external field we obtain the lowest-order correction as well as the third-order correction to the vacuum-polarization potential. The external-field, fermion propagator is also used to obtain an expression for the Delbrück scattering amplitude.