Note on Jackson's formalism of gauge transformation

Abstract

An outline is given of how Jackson may have obtained the inhomogeneous wave equations for the auxiliary functions $\Psi$ and $\mathbf{V}$ in his influential 2002 AJP paper on the transformation from the Lorenz gauge to other electromagnetic gauges. It clarifies the roles of these functions in the calculation of the Coulomb-gauge vector potential ${\mathbf{A}}_C$ by showing that while ${\mathbf{A}}_C$ is given directly $\nabla \times \mathbf{V}$, only the subtraction of $\nabla \Psi$ from the Lorenz-gauge vector potential ${\mathbf{A}}_L$ yields ${\mathbf{A}}_C$.

arXiv commentRewritten and expanded, 4 pages