/sci/ - Science & Math

Can someone tell me why Weinberg (Quantum Theory of Fields 1, chapter 6.4, page 287) states that in this case, the lines on vertices produced by functional derivatives of the S-Matrix would only be internal? As far as I understand it, for a single derivative in ε(x), it produces a further operator O(x) in the time ordering, consisting of a product of fields. These fields can be contracted with the creation/annihilation operators in the initial and final states, connecting the external momenta with the O(x) vertex according to the Feynman rules described earlier in this chapter. The only difference to the normal V potentials in the time ordering is that for O(x), one does not integrate over the spacetime x. I think it must be related to that, but I can't see why and how.