Search

This paper develops a generalized Helmholtz theorem for an arbitrary localized time-varying vector function F(r,t) and shows that the mathematical relations commonly referred to as Maxwell’s equations can be derived from that theorem alone.

In a recent paper Davis formulated a generalized Helmholtz theorem for a time-varying vector field in terms of the Lorenz gauge retarded potentials. The purposes of this comment are to point out that Davis's generalization of the theorem is a version of the extension of the Helmholtz theorem formulated some years ago by McQuistan and also by Jefimenko and more recently by the present author and to show that Davis's expression for the time-dependent vector field is also valid for potentials in gauges other than the Lorenz gaug

The widely used Helmholtz theorem separates an arbitrary vector function into two parts: one is an irrotational component which can be expressed by a scalar function and the other is a rotational part which can only be expressed by another vector function. So it is considered as an incomplete projection of a vector function. In this paper, the generalized theorem is proved. In this theorem an arbitrary vector function is separated into three parts; each can be expressed as a scalar function. It is the complete projection for a vector function in vector wave function space.