I have read these questions:
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.
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.
Which one is right? Can a real free unbound (not bound to a nucleus) accelerated electron absorb/emit a real photon?
In this case, does the virtual photon of the magnetic field help keep the momentum conservation?