  If we develop into perturbation series the evolution operator of the
Heisenberg equation in the infinite dimensional Weyl algebra, say, for the
$\phi^4$ model of field theory, then the arising integrals almost coincide with
the usual Feynman diagram integrals. This fact leads to some mathematical
definitions which, as it seemed to the author, defined dynamical evolution in
quantum field theory in a mathematically rigorous way using the Weyl algebra.
In fact the constructions of the paper are well defined in perturbation theory
only in one-loop (quasiclassical) approximation. A variation of the
construction is related with the Bogolyubov $S$-matrix $S(g)$.
