The QED vertex has two electrons lines joining with a photon line. However, 4-momentum conservation does not allow this process to occur. So why is this process studied? Does it really mean anything to calculate the g-factor of an electron for a process that cannot happen? Only the vertex correction contributes to the g-factor right? But if the other end of the photon line has to connect to something else to conserve 4-momentum, then don't you have to have a diagram with the photon self-energy?