Comment on ‘defining the electromagnetic potentials’

Abstract

Abstract In his recent paper (2020 Eur. J. Phys. 41 045202), Davis makes the claim that potentials and fields are ill-defined in the conventional treatment of electromagnetism. He argues that ‘the usual treatment is ambiguous, with that ambiguity being reflected in the gauge transformation equations’. He then proposes an approach based on two operational versions of Helmholtz’s theorem and claims that his approach does not exhibit gauge freedom and allows a rigourous definition of electromagnetic potentials. Here I argue that Davis’s approach does not provide a more rigours definition of potentials than that provided by the standard approach. Apparently, Davis does not realize that when applying an operational version of Helmholtz’s theorem to Maxwell’s equations, he is not avoiding gauge invariance but tacitly applying it by choosing the particular gauge-condition related to this version of the theorem. The application of the instantaneous Helmholtz’s theorem to Maxwell’s equations is equivalent to the choice of the Coulomb-gauge condition, and the application of the retarded Helmholtz’s theorem to these equations is equivalent to the choice of the Lorentz-gauge condition.