Any good references on the analytic structure of scattering amplitudes?

Question

In papers they often say things about the analytic structure of S matrices - things like resonances are poles on the unphysical sheet, particle channels cause a square root branch cut etc.

I've seen this demonstrated in a couple of simple cases but I was wondering if there was any book/notes where this is talked about in general?

Answer 1

In general analyticity is consequence of causality and unitarity. A classic text is Eden, Landshoff and Polkinghorne The analytic S-Matrix. It focusses on $S$-matrix elements, but discusses the analytic properties of individual Feynman diagrams.