Comment on "How the potentials in different gauges yield the same retarded electric and magnetic fields," by J. A. Heras [Am. J. Phys. 75, 176 (2007)]

TL;DR

This paper critiques Heras's algebraic approach claiming gauge invariance of retarded fields, arguing it lacks explanatory depth and does not replace solving the dynamic equations.

Contribution

It challenges the validity of Heras's algebraic method, emphasizing the importance of solving dynamic equations for understanding gauge invariance.

Findings

Heras's algebraic manipulation is criticized as lacking explanatory content.

The paper emphasizes the necessity of solving dynamic equations for accurate gauge analysis.

It clarifies misconceptions about gauge invariance and causality in electromagnetic potentials.

Abstract

Heras purports to show without solving the requisite dynamic equations how the non-causal term generated by the scalar potential of the Coulomb, Kirchhoff, or velocity gauge is canceled by an equal and opposite term in the contribution to the electric field that is generated by the vector potential. Heras's procedure is criticized as being just an algebraic manipulation that has no explanatory content.