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 ${\varphi }^4$ field theory, avoiding the contributions from anomalous thresholds.

arXiv commentLaTeX file, 23 pages including 22 figures

References in corpus (6)

• Cutkosky Rules for Superstring Field Theory
• Cutkosky rules and perturbative unitarity in Euclidean nonlocal quantum field theories
• Nonlocal vertices and analyticity: Landau equations and general Cutkosky rule
• Causality and Unitarity via the Tree-Loop Duality Relation
• A brief Introduction to Dispersion Relations and Analyticity
• Algebraic cutting equations

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• Hyperbolic Geometry and Closed Bosonic String Field Theory II: The Rules for Evaluating the Quantum BV Master Action
• BRST cohomology of timelike Liouville theory
• Quantum Closed Superstring Field Theory and Hyperbolic Geometry I: Construction of String Vertices
• A Stringy Effect on Hawking Radiation
• Peaks and cusps: anomalous thresholds and LHC physics
• Hyperbolic Geometry of Superstring Perturbation Theory
• Fractional Particle and Sigma Model
• One-loop four-graviton string amplitude at finite ${\alpha }^{\prime }$
• UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox
• Towards Hamiltonian Formalism for String Field Theory and Nonlocality