Unitarity of the Box Diagram

Abstract: The complete proof of cutting rules needed for proving perturbative unitarity of quantum field theories usually employs the largest time equation or old fashioned perturbation theory. None of these can be generalized to string field theory that has non-local vertices. In arXiv:1604.01783 we gave a proof of cutting rules in string field theory, which also provides an alternative proof of cutting rules in ordinary quantum field theories. In this note we illustrate how this works for the box diagram of $\phi^4$ field theory, avoiding the contributions from anomalous thresholds.