Which varieties of Lienard-Wiechert derivation are done correctly?

Question

I stumbled upon the paper https://arxiv.org/abs/0704.1574 which claims:

"In all of the relativistic derivations, retardation effects are neglected, whereas in the original 19th Century derivations of the LW potentials or the corresponding retarded fields, no relativistic effects are considered. There are therefore two independent, logically incompatible, and incorrect, derivations of retarded potentials and their associated fields."

Also they claim the Jefimenko approach is just wrong. They present their own version of Lienard-Wiechert which they claim is better.

The math is complicated. Before I try to follow it, does anybody know whether this is worth doing? Is the author J.H.Field known as a crank who consistently gets things all wrong? Is it known that this particular work is wrong?

Comments

I wouldn't trust the author. In https://arxiv.org/pdf/0706.1661, he claims that QED predicts acausal (instantaneous) effects verified by experiment, mistaking virtual particles language for processes happening in time.

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I haven't noticed any discrepancies in the solutions given in different textbooks. Originally the LW potentials are just solutions of the wave equations with a given source, so it is right. Relativity adds up another way of communicating between different points of space and establishing their true positions in a given reference frame, but in a given RF the space and time are then considered "absolute" even in relativistic case. Relativity changes the formulas of calculations of LW potentials in a moving reference frame if they are known in a resting RF.

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He claims that Lienard's solution and Feynman's solution are equivalent.

But that Jefimenko's solution is not equivalent and that derivations of it have mathematical mistakes which he claims to have sorted out.

His own solution with different assumptions is not the same as either of the others. That is not standard physics, and it could be correct if his starting assumptions are correct and if he did his math correctly. I'm not clear how different his results are or whether the difference is testable experimentally today, or whether it has been tested.

His claims about the other versions could be correct independent of his own nonstandard version.