Static field from ensemble of photons

[patdriess]

Hi,

In QED it is stated that an EM field can be written as a sum of quantized oscillators (the photons).
In "classical" Electrodynamics, it can also be shown that the EM field decomposes into normal modes.

But both the quantized oscillators (in the Heisenberg picture) and the classical normal modes have a phase that oscillates with time. This goes also, as far as I know, for the longitudinal photons.

Do you know of a paper (or a book) that shows or a static electric field (generated by a static charged source)
or a stationary magnetic field (generated by a stationary current) can be
written in terms of a superposition of time-varying operators or normal modes.

 

[vanhees71]

A heavy charged particle, probed by light charged particles can be approximately described by its Coulomb-like field. To derive this, you need a summation over infinitely many Feynman diagrams, which however all correspond to the same (leading) order in the electromagnetic coupling constant (soft-photon resummation). For an excellent treatment, see

Weinberg, The Quantum Theory of Fields, Vol. 1