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I've frequently heard the statement that the only singularities of the S-matrix in QFT correspond to things like the existence of bound states and the possibility of multi-particle production. I'm certain I've seen this worked out before, but for some reason I can't find any place that explicitly shows how these singularities arise in the S-matrix for these cases. Can someone point me to a reference for this, or explain why this is the case?

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  • $\begingroup$ Weinberg's textbook The Quantum Theory of Fields Volume 1, section 10.2 "Polology" has a great discussion of this. $\endgroup$ – Seth Whitsitt Oct 19 '19 at 16:47

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