Comment on work of Yang and Nevels "Direct, analytic solution for the electromagnetic vector potential in any gauge" (arXiv:2507.02104)

TL;DR

This paper critically analyzes a recent electromagnetic potential solution, demonstrating that it relies on mathematically invalid steps and providing counterexamples that challenge its validity.

Contribution

It offers a detailed critique of the solution method in the referenced work, highlighting mathematical errors and invalid assumptions.

Findings

The solution is based on illegal mathematical operations.

Counterexamples show the solution does not satisfy key equations.

Direct calculations in different gauges reveal inconsistencies.

Abstract

In the Comment the procedure for obtaining a solution for the electromagnetic potential, presented in the cited work arxiv:2507.02104, is analyzed. It is shown that the solution obtained by the authors is based on some mathematically illegal operations. This argument is supported by a counterexample to equation (10) of the cited work. Direct calculations of the potentials in the Lorenz and Coulomb gauges show that equation (10) is not satisfied.