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Compton scattering is usually described two Feynman graphs (in the second-order perturbative expansion of scattering matrix) that can be described in the following way:

  1. annihilation of a photon-electron pair, propagation of a virtual electron, creation of a photon-electron pair (a)
  2. exchange graph

However, if one draws all second-order Feynman graphs in the second order (regardless of their physical meaning), among others one obtains a graph (b): creation of real electron-photon pair in the first (left) vertex, propagation of virtual positron and annihilation of real electron-photon pair in the second (right) vertex (so that it is not a vacuum graph; I assume that time flows from left to right). Why isn't this graph considered physical?

enter image description here

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    $\begingroup$ Did you mean a diagram with no external legs? $\endgroup$
    – Danu
    May 10, 2014 at 16:32
  • $\begingroup$ Sorry, I didn't put it the right way: all lines (except for one virtual electron line between the vertices) correspond to real particles. Therefore in each vertex two real and one virtual line connect. $\endgroup$
    – Paweł
    May 10, 2014 at 16:51
  • $\begingroup$ I'm confused by the wording. Can you draw the diagrams and upload a pic? $\endgroup$
    – Prahar
    May 10, 2014 at 17:23

1 Answer 1

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When counting all possible graphs you need to keep the structure of the internal propagators consistent. You switched the direction of the internal arrows on the propagator of the second graph. The choice of writing the internal propagator pointing to the right is arbitrary and you could easily well have made the opposite choice, but you need to be consistent. Once you write down the first diagram you are not allowed to write (b).

There are two unique diagrams, the one you showed and the one with the photon lines crossed. The other two possibilities (one of which you show above) are accounted for by "swapping the vertices", which are taken into account through symmetry factors of each of the two unique diagrams.

However, its important to keep in mind that these "fairy-tails" (as Sidney Coleman called them) are just mnemonics to remember which graphs contribute. So don't be too heart-broken if the rules seem ad-hoc to you at first.

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  • $\begingroup$ I do not know feynman diagrams, so this might be a trivial question, but also in the diagram $a$, shouldn't real particle created on the right vertex go below because of the momentum conservation ? I mean, I do not whether it goes to up or down have any meaning in this diagram, but it would be much more meaningful in that, I think. $\endgroup$
    – Our
    Oct 14, 2018 at 5:10

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