QED Picture of static EM Fields

[physwiz222]

TL;DR Summary

If the picture of electrostatics being due to electrons exchanging virtual photons isnt correct whats the actual QED description of Static EM Fields.

Hello I know in QED the EM field is quantized and described in terms of photons and Classical EM Waves are described as emerging from coherent states of the field. I also heard that Electrostatic and Magnetostatics forces are mediated by Virtual Photons so 2 electrons repel by exchanging virtual photons so the explanation seemed satisfying.

However I learned that Virtual Photons are just a mathematical trick and an artifact of Perturbation Theory and dont really exist and this picture of 2 electrons physically exchanging discrete particles is not correct. If this is the case what is really the Electrostatic or Magnetostatic or even Faraday Quasistatic Field in QED if it isnt simply the exchange of Virtual Photons. Is it maybe just non particle excitations of the EM field is it just stronger Vacuum Fluctuations. I dont know. This might be a tangent but is it possible for Quantum fields in general to have Non Particle excited states. By this I dont mean superpositions of particle states I am talking about a Field State which has nothing to do with particles whatsoever.

I havent really found any great sources they all say the same Virtual Particles dont exist they are only calculational tools for Feynman Diagrams and arent real objects but never say what Static fields like Electrostatic Fields in QED actually are. There are satisfying explanations for EM Waves and Vacuum fluctuations without Virtual Particles but not really any for Electro, Magneto, or Quasistatic Fields.

Keep in mind I want a Virtual Photon FREE picture of it isnt already obvious for static EM fields. I am also asking this because shouldnt the Fundamental Theory of Matter and Light QED have something to say about Electrostatics and Magnetostatics along with Quasistatic Faraday Fields as well.

 

[vanhees71]

In the picture of perturbative QED the static Coulomb field emerges due to the necessity to resum an infinite number of Feynman diagrams to take into account consistently at a given order in the coupling constant due to "soft photons".

Another approach is a more careful analysis of what is an asymptotic free state in the context of the long-range nature of the electromagnetic interaction, i.e., due to the masslessness of the electromagnetic field. As it turns out the naive picture of a "naked/bare charged particle" is flawed. The "true asymptotic states" are rather what's called "infra-particle states". These describes that a charged particle always carries its own long-ranged electromagnetic Coulomb field around it.

There are these popular-science metaphors, known as "virtual particles", but what's behind this is just a pragmatic language about what's in the mathematical formalism of perturbative quantum field theory. The Feynman diagrams are just very clever notations for the corresponding formulae of the equations allowing to calculate physically observable facts of particles, i.e., cross sections for scattering events, describing the probability rates for transitions from one asymptotic free state to another. In this metaphorical picture with some grain of salt you can say that a true asymptotic free state of a charged particle is a state of a bare charged particle surrounded by a "cloud of virtual photons", which is just another word for a charged particle surrounded by its own electromagnetic field.

 

[physwiz222]

In the picture of perturbative QED the static Coulomb field emerges due to the necessity to resum an infinite number of Feynman diagrams to take into account consistently at a given order in the coupling constant due to "soft photons".

Another approach is a more careful analysis of what is an asymptotic free state in the context of the long-range nature of the electromagnetic interaction, i.e., due to the masslessness of the electromagnetic field. As it turns out the naive picture of a "naked/bare charged particle" is flawed. The "true asymptotic states" are rather what's called "infra-particle states". These describes that a charged particle always carries its own long-ranged electromagnetic Coulomb field around it.

There are these popular-science metaphors, known as "virtual particles", but what's behind this is just a pragmatic language about what's in the mathematical formalism of perturbative quantum field theory. The Feynman diagrams are just very clever notations for the corresponding formulae of the equations allowing to calculate physically observable facts of particles, i.e., cross sections for scattering events, describing the probability rates for transitions from one asymptotic free state to another. In this metaphorical picture with some grain of salt you can say that a true asymptotic free state of a charged particle is a state of a bare charged particle surrounded by a "cloud of virtual photons", which is just another word for a charged particle surrounded by its own electromagnetic field.

So its basically just a modified quantum form of a classical Electrostatic Field. So I can visualize an electron creating an EM field state in a fuzzy superposition of classical electrostatic field configurations.

 

[LittleSchwinger]

So its basically just a modified quantum form of a classical Electrostatic Field. So I can visualize an electron creating an EM field state in a fuzzy superposition of classical electrostatic field configurations.

To low orders. At higher orders the electromagentic field about the electron will contain corrections from interactions with the electron field itself, involving electron-positron bubble terms.