Schrödinger equation in quantum field theory with nonlocal interaction

It is shown that a finite and unitary $S$-matrix describing the nonloeal interactions of quantized fields is a solution to the Cauchy problem of an evolution equation (Schrödinger equation in the interaction representation with imaginary time, i.e., in Euclidean metric) with retardation. There is no need to introduce any additional degrees of freedom compared with the ordinary Fock space of physical particles.