  We conjecture that the renormalized perturbative $S$-matrix of quantum field
theory coincides with the evolution operator of the standard functional
differential Schrodinger equation whose right hand side (quantum local
Hamiltonian) is understood as an element of an appropriate quantization of the
Poisson algebra of classical field theory Hamiltonians. We show how to
construct a quantization of this algebra, close to the algebra of differential
operators on infinite dimensional space, but seemingly not appropriate for
quantum field theory.
