Final answer:
In Quantum Electrodynamics (QED), static electric fields are represented in the vacuum expectation values of the field operators and involve virtual photons. Direct quantum-level measurements of static E-fields are focused on observable consequences like forces and energy shifts, rather than direct field measurements.
Step-by-step explanation:
The quantum description of electrostatic fields is indeed different from that of propagating electromagnetic waves. Typically, a quantum field theory of electromagnetism, such as Quantum Electrodynamics (QED), deals with dynamical, oscillating fields described by photons. However, a static electric field, like the one created by a stationary charge, is represented in QED by the vacuum expectation value of the electromagnetic field operator in a state with a definite number of charges.
Quantum mechanically, even the static electric field would be composed of virtual photons, which cannot be directly observed. The experimental measurements of static electric fields at the quantum level typically focus on the forces and potential energies associated with point charges or the atomic transitions influenced by static fields, rather than the field itself. In these cases, the quantized nature of the field is implicit in the way particles interact with the field.
The 'zero frequency mode' would indeed correspond to a steady, unchanging field in the classical limit. In quantum field theory, vacuum fluctuations and virtual particles still imply a sort of dynamism even in what we classically describe as a static field. However, it's important to note that a full and direct quantum measurement of the static E-field is a complex challenge and the focus is usually on its observable consequences, such as energy shifts, rather than on a field vector measurement.