The field-forms used in electrodynamics including classical
electrodynamics, quantum electrodynamics, and quantum chromodynamics is
based on Coulomb's point-to-point fields. The lienard-wiechert
potentials (barut, "electrodynamics and classical theory of fields and
particles", dover, 1980, in ch. 5, 'radiation and radiation reaction')
measure the distance between charges in motion as the 3-D distance
directly between the actual charge points. Now this is a very natural
thing to do, and follows from Coulomb's macroscopic electrostatic
experiments. It's important to realise Coulomb performed these
experiments around the time of the French revolution or when Australia
was 'discovered' by Captn James Cook!!. That's ok, but are they
correct at microscopic, atomic, and nuclear levels of interaction?
Should QFT be using coulomb-like fields?

Von Hippel ("Dielectric and waves", Dover, 1962, p45f) uses the
well-known Hertzian potentials to obtain the radiated energy density
(per unit time) in the far-field of an electric dipole antenna. barut
gives the power = 2*e^2*v_dot^2)/(3*4*pi*c^3) The rotating vectors of
the hertzian potential are in the form of a time exponential
well-klnown to mathematicians from the study of differential wave
equations and their general solutions: exp{j*w*(t-r/v)}. Now these
'fields' (actually potentials and NOT electric and magnetic fields
as per Maxwell's equations) suggest a FIXED reference rather than a
moving reference. It was this form of potential (together with a
suggestion from my ph.d supervisor) that led me to attempt to use
centre-of-motion fields. It is only then that the electronic
interaction in atoms can be effectively solved using the Maxwell field
equations.