I am presently slogging through an introductory text on QFT (a Christmas present - does that officially make me a nerd?) and I have gotten as far as the Dyson expansion of the S operator and Wick's Theorem. The author dismisses all first-order terms of the expansion as being represented by single-vertex Feynman diagrams, which are unphysical. As an example, he uses the interaction where an electron and positron enter and a photon leaves, which is not possible because a real photon cannot carry away the 4-momentum the massive particles entered with. However, I am under the impression that an electron and positron annihilating to produce a high-energy photon is an experimentally observed interaction. Where am I going wrong?