  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.
