It is rather obvious for me that the generalized optical theorem (see e.g. Peskin&Schroeder) must hold for S-matrix elements for fermions as it is directly related to the unitarity of the S-matrix. But what about the generalization by Cutkosky to individual Feynman graphs? Do Cutkosky rules hold for any Feynman graph in arbitrary perturbative quantum field theory, and if yes, do they always look the same? I am asking because the derivations I am aware of (circling rules) are performed for scalars. What about the generalization to finite temperature field theory (Weldon et.al.)?


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