One Loop Vacuum Polarization without Infinities
  A technique for avoiding infinite integrals in the calculation of the one-loop diagram contribution to the vacuum polarization component of an atomic energy level is presented. This makes renormalization unnecessary. Infinite integrals do not occur because, as it is shown, no delta functions are required for the Green's functions. Thus there are none to overlap. This procedure is shown to produce the same formula as the one obtained by dimensional renormalization. 
A.A. Broyles