Differential operators on infinite dimensional space and quantum field theory

Abstract

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.