Checking for new eprints, three papers by P. J. Cote and M. A. Johnson caught my attention: (A) New perspectives on classical electromagnetism (arXiv:0903.4104v2), (B) On the peculiarity of the Coulomb gauge (arXiv:0906.4752v1), (C) Groupthink and the blunder of the gauges (arXiv:0912.2977v1). The main point of these papers seems to be that the exploitation of gauge freedom in electromagnetism is questionable. Specific objections are raised to steps in standard derivations using Lorentz and Coulomb gauges. For example, the title of paper B refers to the non-locality of potentials in the Coulomb gauge and some remarks on the matter quoted from J. D. Jackson’s classic textbook.
The papers themselves border on crankery, which is a bit alarming since the authors are affiliated with the army, but are at least wrong in instructive ways. Electromagnetism is manifestly gauge invariant and there are no genuine causality problems in the Coulomb gauge since the non-local potentials are not physically meaningful quantities in and of themselves. Only quantities such as electromagnetic fields and holonomy integrals, which do not contain gauge degrees of freedom, have physical meaning. Since the authors raise concerns about the causality of Coulomb-gauge potentials and Gauss’ law applied to dynamical fields, it is ironic that there are refutations that predate their arguments. In direct connection with the remark quoted in paper B from J. D. Jacksons textbook, Jackson also refers the reader to a paper by Brill and Goodman (1967) that sorts out the causality issues.
In fact, it is interesting to see in detail how the causality issues are avoided, so Brill and Goodman’s paper is well worth a read. Related points are discussed by Jackson (2002), who works out explicit expressions for the gauge transformations that relate different gauge choices (including a gauge I had not heard about before in which potentials propagate at a given arbitrary speed), and Heras (2007), who shows explicitly that different gauges yield the same electric and magnetic fields. Hnizdo (2004) works out the details of the potentials for a moving point charge. As calculations in electrodynamics can be tedious and involve easy-to-forget subtleties connected to delta functions and retardation effects, it is very useful to see the equations worked out.
O. L. Brill and B. Goodman. Causality in the Coulomb Gauge. Am. J. Phys. 35:832 (1967) [Available here]
J. D. Jackson. From Lorenz to Coulomb and other explicit gauge transformations. Am. J. Phys. 70:917 (2002)
J. A. Heras. How the potentials in different gauges yield the same retarded electric and magnetic fields. Am. J. Phys. 75:176 (2007)
V. Hnizdo. Potentials of a uniformly moving point charge in the Coulomb gauge. Eur. J. Phys. 25:351 (2004)