  Divergences that arise in the quantization of scalar quantum field models by
means of a lattice-space functional integration may be attributed to a single
integration variable, and this fact is demonstrated by showing that if the
integrand for that single integration variable is appropriately changed, then a
perturbation expansion becomes order-by-order finite and divergence free. The
paper concludes with a brief review of a current proposal of how an auxiliary,
nonclassical potential added to the lattice action of a relativistic scalar
field quantization may automatically render an analogous change of the
integrand, and thus may lead, as well, to nontrivial and divergence-free
results.
