  The functional renormalization group flow of a scalar field theory with
quartic couplings and a sharp spatial momentum cutoff is presented in
four-dimensional Minkowski space-time for the bare action by retaining the
entanglement of the IR and the UV particle modes. It is argued that the open
interaction channels have to be taken into account in quantum field theory
defined by the help of a cutoff, and a non-perturbative UV-IR entanglement is
found in closed or almost closed models.
