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Electrically charged particles interact with each other via the exchange of a photon (as it is the exchange particle of the electromagnetic force).

When considering, e.g., the Compton-effect, where a photon interacts with an electron and ionizes the atom, do they also interact via a virtual photon?

They must I would say as there is no other possibility, I just want to make sure it is not the initial photon itself (alone)?

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Unlike two electrons, a photon and an electron can interact directly with each other. In other words, the photon couples to the electron. In the language of quantum field theory, in the set of the building blocks of the Feynman diagrams that describe different processes, there exists a vertex where an electron and a photon meet and evolve into an outgoing electron. So, for an electron and a photon to interact, they don't need to exchange any other particles. Of course, there are processes where an electron and a photon can interact with each other via exchanging some particles, but, there exists a direct way for them to interact as well. In Compton scattering, an electron and a photon interact with each other to give off a virtual electron which then decays into an outgoing photon and an outgoing electron. Notice that this intermediate virtual electron is not the particle via which the photon and the electron are interacting. They already interacted and gave birth to the intermediate virtual electron which then decays into another electron and a photon--the products that we detect.

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    $\begingroup$ Just to add to the answer, this vertex (where 2 fermions and a photon meet) is the only vertex in QED. $\endgroup$ – Vangi Aug 16 at 11:17
  • $\begingroup$ Thanks for the answer! Relative to the comment: What about quarks in QED or are they not contained there? $\endgroup$ – Ben Aug 16 at 11:33
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    $\begingroup$ @Ben No, the only fields in QED are the electromagnetic fields (photon) and the electron field (electron). $\endgroup$ – Dvij Mankad Aug 16 at 11:37
  • $\begingroup$ but quarks are fermions :) $\endgroup$ – Ben Aug 16 at 12:24
  • $\begingroup$ @Ben Yes, but QED is not the theory of all fermions. :) There are many fermions in the Standard Model and only the electron (or, if you wish, the muon, and the tau) is in QED. In the Standard Model, there are neutrinos as well as quarks. They are not in QED. $\endgroup$ – Dvij Mankad Aug 16 at 12:27

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