  We give a conjectural way for computing the $S$-matrix and the correlation
functions in quantum field theory beyond perturbation theory. The basic idea
seems universal and naively simple: to compute the physical quantities one
should consider the functional differential Schrodinger equation (without
normal orderings), regularize it, consider the regularized evolution operator
in the Fock space from $t=T_1$ to $t=T_2$, where the interval $(T_1,T_2)$
contains the support of the interaction cutoff function, remove regularization
(without adding counterterms), and tend the interaction cutoff function to a
constant.
  We call this approach to QFT the No-Counterterm approach. We show how to
compute the No-Counterterm perturbation series for the $\phi^4$ model in
$R^{d+1}$. We give rough estimates which show that some summands of this
perturbation series are finite without renormalization (in particular, one-loop
integrals for $d=3$ and all integrals for $d\ge 6$).
