I was reading the following book/series of lectures located here http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf; it's an introduction to quantum field theory. I'm at the part about vacuum polarization in QED, regularization, and renormalization.
On page 179 the author gives the one-loop corrections to the effective electron's electric charge as a function of the momentum (they also state it as the effective fine structure constant/effective momentum dependent potential, etc). Here's my question; a little bit later on the author says that the loop corrections to the effective charge/running fine structure constant/etc are known to all orders. This would imply that the photon propagator is known to all orders in perturbation theory (this is also implied by the diagram that they've drawn on the same page). So the question is; is this accurate? Is the EXACT photon propagator in quantum electrodynamics?
EDIT: I'd just like to clarify what exactly I am asking. I am not asking if QED is a complete physical theory. It most certainly is not! A Landau pole exists at arbitrarily high energies (absurdly high energies; before posting this question I searched for similar questions and I remember reading something about the Landau pole in QED being in excess of 100 orders of magnitude larger than the plank energy), and more to the point at energies far lower than the Landau pole you ought to use electroweak theory instead. What I am asking is whether the propagator for the photon is known to ALL orders in perturbation theory (one loop corrections, two loop corrections, three loop corrections, four loop corrections, etc). I am not asking whether or not such a propagator is part of a physically complete QFT.