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What is the full quantum mechanical description of the statement from classical electromagnetism "the electric field of a uniformly charged infinite flat plane is constant"?

By "full" I mean that I'm not interested in a semiclassical description, rather I want an explanation with the EM field quantized.

The purpose of my question is to understand whether force carriers (photons) play a role in this description. Specifically:
* Is it true that the constant field is equivalent to photons being constantly emitted from the flat plane such that their net sum interaction with a test positive charge is to give it a constant amount of momentum? (At least, is that the most probable result?)
* Could one even talk about photons for a non-radiative field?

This question is similar to this and this, but I can't find answers to my question in those questions. The answers that appear there address the following issues: *what are particles and force carriers in quantum field theory? *how to derive the Coulomb force from a scattering amplitude calculation? But I don't see any reference as to what is the description (or ontology) of the systems in QED terms. I don't mind if the answer will address the simpler system of a point charge and its Coulomb field.

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Lior
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  • In the Coulomb gauge non-radiative fields enter through Coulomb potentials and photons (associated with transverse fields) are not involved. – Urgje Sep 23 '15 at 10:18
  • The full quantum mechanical description of a system that doesn't exist is "Such a system doesn't exist." The correct classical description of a flat charged plate of finite dimension is that the electric field close to the surface of the plate is (almost) constant and far away from the plate it behaves very similar to that of a point charge. There is, unfortunately, no simple quantum field theoretical description of a flat plate, since one would have to model the atomic structure of the plate, first, which is enormously complex. Constant fields do not mean that photons are being emitted. – CuriousOne Sep 23 '15 at 10:18
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    possible duplicate of Deriving the Coulomb force equation from the idea of photon exchange? – John Rennie Sep 23 '15 at 10:44
  • I've linked a Q/A that shows how QED describes a static field. Your example of an infinite plate seems to be just a particular example of a static field. – John Rennie Sep 23 '15 at 10:45

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