  Nonrenormalizable scalar fields, such as \varphi^4_n, n\ge5, require
infinitely many distinct counter terms when perturbed about the free theory,
and lead to free theories when defined as the continuum limit of a lattice
regularized theory restricted only to arbitrary mass and coupling constant
renormalization. Based on the proposal that functional integrals for
interacting nonrenormalizable models do not reduce to the expression for the
free field functional integral as the coupling constant vanishes -- a proposal
supported by the fact that even the set of classical solutions for such models
does not reduce to the set of free field solutions as the coupling constant
vanishes -- it has been conjectured that for nonrenormalizable models the
interaction term acts partially as a hard core eliminating certain fields
otherwise allowed by the free theory. As a consequence, interacting models are
continuously connected to a pseudofree theory that takes into account the hard
core as the coupling constant vanishes, and this general view is supported not
only by simple quantum mechanical examples as well as soluble but
nonrelativistic nonrenormalizable models. The present article proposes a
pseudofree model for relativistic nonrenormalizable models about which it is
argued that a perturbation expansion of the interaction is term-by-term
divergence free.
