  We rigorously define renormalized evolution operator of the Schr\"odinger
equation in the infinite dimensional Weyl-Moyal algebra for any time interval
for arbitrary Hamiltonian depending on time. We state that for renormalizable
field theories, in the interaction representation, and for the time interval
being the full real axis, our construction yields standard renormalized
$S$-matrix and Green functions of perturbative quantum field theory.
