Static field from ensemble of photons

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SUMMARY

The discussion focuses on the representation of electromagnetic (EM) fields in Quantum Electrodynamics (QED) and classical Electrodynamics. It establishes that both quantized oscillators (photons) and classical normal modes exhibit time-oscillating phases. The inquiry seeks references that demonstrate how static electric fields from stationary charges or stationary magnetic fields from currents can be expressed as superpositions of time-varying operators or normal modes. The discussion highlights the necessity of summing over infinitely many Feynman diagrams to derive the Coulomb-like field of a heavy charged particle, emphasizing the work of Steven Weinberg in "The Quantum Theory of Fields, Vol. 1" as a key resource.

PREREQUISITES
  • Quantum Electrodynamics (QED) principles
  • Classical Electrodynamics concepts
  • Feynman diagram techniques
  • Understanding of electromagnetic coupling constants
NEXT STEPS
  • Study the derivation of static electric fields in QED
  • Explore the concept of soft-photon resummation
  • Read "The Quantum Theory of Fields, Vol. 1" by Steven Weinberg
  • Investigate the relationship between time-varying operators and static fields
USEFUL FOR

Physicists, particularly those specializing in quantum field theory, researchers in electromagnetic theory, and students seeking to deepen their understanding of the relationship between static and dynamic electromagnetic fields.

patdriess
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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.
 
Physics news on Phys.org
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
 

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