Derivation of the Lorentz potentials

The article [Schwab et al., 1996] on semantics of the irrotational component of the magnetic vector potential inspired the following alternative derivation of the expressions for the magnetic field, H, and the electric field, E, in terms of the Lorentz potentials. The artifice of the Lorentz gauge is not used in this derivation. Instead, the Lorentz potentials are required to satisfy differential equations akin to those satisfied by the Coulomb potentials. The Lorentz vector potential, A_L, is constructed by adding what turns out to be an irrotational vector, A_irr, to the Coulomb vector potential, A_C. The Lorentz scalar potential, φ_L, is constructed by adding a scalar, φ, to the Coulomb scalar potential, φ_C