Abstract
We overview recent results on the mathematical foundations of Cutkosky rules. We emphasize that the two operations of shrinking an internal edge or putting internal lines on the mass-shell are natural operation on the cubical chain complex studied in the context of geometric group theory. This together with Cutkosky's theorem regarded as a theorem which informs us about variations connected to the monodromy of Feynman amplitudes allows for a systematic approach to normal and anomalous thresholds, dispersion relations and the optical theorem. In this report we follow [1] closely.
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