Causality and Unitarity via the Tree-Loop Duality Relation

Abstract

The tree-loop duality relation is used as a starting point to derive the constraints of causality and unitarity. Specifically, the Bogoliubov causality condition is ab initio derived at the individual graph level. It leads to a representation of a graph in terms of lower order cut graphs. Extracting the absorptive part gives then the general unitarity relation (Cutkosky rule). The derivation, being carried out directly in momentum space, holds for any local (polynomial) hermitian interaction vertices. This is in contrast to the technical difficulties arising from contact terms in the spacetime approach based on the largest time equation.

23 pages, 5 figures, typos corrected, some added references and concluding remarks, published version

References in corpus (4)

• From loops to trees by-passing Feynman's theorem
• Towards gauge theories in four dimensions
• A Tree-Loop Duality Relation at Two Loops and Beyond
• On the singular behaviour of scattering amplitudes in quantum field theory

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• What is the $i\epsilon$ for the S-matrix?
• Geometrical approach to causality in multi-loop amplitudes
• Causal representation of multi-loop Feynman integrands within the loop-tree duality
• Loop-tree duality from vertices and edges
• Quantum algorithm for Feynman loop integrals
• Unitarity of the Box Diagram
• Automatic computation of Feynman integrals containing linear propagators via auxiliary mass flow
• Universal opening of four-loop scattering amplitudes to trees
• Initial value problem in string-inspired nonlocal field theory
• Exposing the threshold structure of loop integrals
• Asymptotic expansions through the loop-tree duality
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes