Unitarity of the Box Diagram

TL;DR

This paper demonstrates a proof of unitarity for the box diagram in $$ field theory using cutting rules adapted for string field theory, avoiding anomalous threshold complications.

Contribution

It provides a novel proof of cutting rules for string field theory and applies it to the box diagram in $$ theory, extending previous methods.

Findings

Proof of cutting rules for string field theory.

Application to the box diagram in $$ theory.

Avoidance of anomalous threshold contributions.

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.