Extraction of Singularities from the S Matrix

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Abstract
Two methods are described for extracting triangle singularities from matrix elements. The first is comparatively simple but involves the use of off‐mass‐shell amplitudes; the second is rather involved. A proof of the Cutkosky discontinuity formula is given independent of perturbation theory, and it is shown that the Riemann‐sheet properties of the singularity in the physical region agree with perturbation theory. The connection between this and a causality requirement is discussed. The relevance of the work to practical computations is explained.