Field energy of/from virtual Photons

Question

I have a slightly out-of line question:

Consider a single electron (or it's current if you please) The EM field surrounding it will (no doubt) have an EM field energy (T) to go with.

The standard description of interaction is by exchanging a virtual photon. (For simplicity suppose, that only one virtual photon (of arbitrary momentum) can be exchanged)

Question: Is there any way to express the EM field energy "in terms of" virtual photons???

Line A: Every virtual photon has energy-momentum. The EM field energy-momentum is some weighted sum over all virtual photons.

Line B: A photons energy-momentum is very different from the EM field energy, because T ~ FF. But what can be said about the EM T of a single photon?

Line C: Your choice

NOTE: Please note that I own a PhD in physics, so you can answer on any level you like.

Answer 1

The assumption that one can express the energy of an electric field in terms of energy carried by separate virtual photons is fundamentally misguided. A virtual photon is a mathematical object that plays a role in calculating various physical quantities by making use of a perturbation series. One formally assigns energy and momentum to such objects, but what matters on a physical level is only the result of the calculation. Therefore it doesn't make much sense to talk about virtual photons in this way.

Answer 2

«Question: Is there any way to express the EM field energy "in terms of" virtual photons???»

No. The electromagnetic field is a physical system made of real photons not of virtual photons. The energy of the electromagnetic field is given by

$$H_\mathrm{rad} = \sum_r \hbar w_r a_r^\dagger a_r$$

And virtual photons have nothing to do with real photons