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I have read these questions:

Can a free electron absorb a virtual photon even though it cannot absorb an ordinary photon?

Where Michael Seifert says:

It is entirely possible for a real electron to emit a virtual photon and remain on its own mass shell; this is exactly what happens in the classic Feynman diagram with two "real" electrons exchanging a virtual photon. The only reason that conservation laws prohibit a "real" electron from emitting a "real" photon is that it is impossible for all three four-momenta (electron before, electron after, and photon) to simultaneously lie on their respective mass shells.

Can an accelerated "free" electron absorb a photon?

Where Anna V says:

Total absorption would mean an incoming photon+ electron , and outgoing only an electron. This cannot happen because the electron has a fixed mass and does not have excited states to absorb all the energy of the photon. If the outgoing (or incoming) photon becomes virtual, connecting with an electric or magnetic field, then the kinematics has to include the originator of the field in energy momentum considerations, and the electron can absorb all the energy of the incoming photon the energy/momentum balance in its rest mass system taken up by the generator of the field that gave the virtual photon.

So one says that for an accelerating free unbound (so not bound to a nucleus) electron it is possible to completely absorb a real photon, if the electron interacts with the magnetic field's virtual photons, and the momentum conservation is kept by the virtual photons of the magnetic field.

The other one says, it is not possible. Because for the four-momenta for a real electron before, after and real photon, they cannot lie simultaneously on the mass shell.

Question:

  1. Which one is right? Can a real free unbound (not bound to a nucleus) accelerated electron absorb/emit a real photon?

  2. In this case, does the virtual photon of the magnetic field help keep the momentum conservation?

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    $\begingroup$ you are misapprehending the question you quote, a free electron is not accelerating, it is in an inertial frame, and acceleration does not belong to an inertia frame, but needs an input dp/dt specific boundary conditions . also the two different answers to the different questions are saying the same thing in different words. $\endgroup$ – anna v Sep 7 '18 at 17:39
  • $\begingroup$ @annav can you please tell me if an unbound electron, accelerating in a magnetic field, can or cannot emit/absorb a real photon? $\endgroup$ – Árpád Szendrei Sep 7 '18 at 17:42
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    $\begingroup$ if it is accelerating there exists a third participant in the interaction and the energy momentum balance can happen between the three inputs , the electron the photon and the originator of the magnetic field $\endgroup$ – anna v Sep 7 '18 at 17:44
  • $\begingroup$ @annav thank you so you are saying that in this case the originator of the magnetic field (I assume another charge) will help keep the momentum conservation? And so the electron will be able to emit/absorb a real photon? $\endgroup$ – Árpád Szendrei Sep 7 '18 at 17:46
  • $\begingroup$ Yes, it is simple if one writes feynman diagrams for the specific situation, like the photon pair production which also needs a field en.wikipedia.org/wiki/Pair_production#Cross_section .i.stack.imgur.com/kBXX5.jpg , a virtual photon represents the field $\endgroup$ – anna v Sep 7 '18 at 18:20

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