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.
