Extraction of Singularities from the S Matrix
P.V. Landshoff, D. Olive · Journal of Mathematical Physics · 1966
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.