In another question, I was asking about the interaction between photons and electrons. It was suggested that in compton scattering there is no particle to "mediate" the force. The tree-level diagrams in compton scattering of photon and electron are

compton scattering diagrams

My questions are:

  1. Why does one not consider the electron to mediate a force between photon and electron? Clearly there is a force, as the two particles scatter, therefore they interact.

  2. Why do force-mediators have to be bosons in general?

If possible I would really prefer an answer which is not just heuristics/storytelling and is grounded in the theory itself. enter image description here Edit: A helpful link to essentially the same question has been shared. However, I don't see how the answers are satisfactory to rule out electrons as the force-carrier in the diagrams above. I will explain for each answer.

In the first answer, by Ben Crowell, I see two issues: The spins can add up: $1 - 1/2 = 1/2$, but more importantly, Feynman diagrams are a counting technique to get the combinatorics right. They are strongly suggestive of interactions, but there is no inconsistency if angular momentum is not conserved in a diagram. Otherwise, supposing my spin addition is somehow wrong (which I suspect) then naively, we could use this to predict that electrons and photons do not interact because their mediator would have to be an electron, which would violate angular momentum conservation at tree level, and behold! that prediction would be wrong.

In the second answer by Adam, it suggests that the opposite is true, namely that electrons can be thought of as force carriers.

In the third answer by Trimok, it only addresses interactions between fermions so that's just not the case here.

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    $\begingroup$ Does this answer your question? Why are all force particles bosons? $\endgroup$ Dec 31 '19 at 12:33
  • $\begingroup$ Thanks for the reference, that helps, and it didn't come up in my search. It doesn't answer my question though; I'll edit the question now to explain why. $\endgroup$ Dec 31 '19 at 12:53
  • $\begingroup$ I think you are putting too much emphasis on nomenclature. Interactions generated by connections of the gauge theory are called forces. There is nothing more to it than that. $\endgroup$ Dec 31 '19 at 13:28
  • $\begingroup$ The title question (v3) seems to be a duplicate. If the previous answers are wrong, consider to put a bounty for better answers. $\endgroup$
    – Qmechanic
    Dec 31 '19 at 13:40
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    $\begingroup$ I think you're trying to look for consistency with the word "force" here where there is none (cf. obligatory xkcd). 1. Your "force" between electron and photon "mediated by the electron" is called Compton scattering. You could also call it "Compton force interaction". What difference does it make? 2. Your objection to Ben's answer to the other question misunderstands Ben's answer: He's saying that only a boson can mediate a force between two particles with the same spin such that the outcome of the interaction is the same (kind of) two particles. $\endgroup$
    – ACuriousMind
    Dec 31 '19 at 13:45