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Causality and unitarity via the tree-loop duality relation. (English) Zbl 1396.81184
Summary: 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.

MSC:
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T18 Feynman diagrams
81U05 \(2\)-body potential quantum scattering theory
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