Hertzian electromagnetic potentials

Abstract

The general properties of the Hertzian electromagnetic potentials and their gauge transformations, recently given by Nisbet, are re-derived in tensor form appropriate to the space-time of special relativity. There appears to be a considerable gain in conciseness and comprehensibility of the general results, although it is recognized that Nisbet’s forms may be those suited to particular applications. Whittaker’s scalar potentials are briefly considered. The theory refers exclusively to flat space-time because the results require covariant differentiation to be commutative, but it is formulated in terms of any curvilinear co-ordinates in such space-time.

Spinor and Hertzian Differential Forms in Electromagnetism

“…Finally Hertz and Debye potentials intervene to tackle electromagnetism in General Relativity [23,40]. To check the contribution of hertzian differential forms to these problems will be an interesting job.…”

“…Hertz potentials known from the start of electromagnetic theory [36] do not seem to have been extensively used in spite of noticeable exception [3,37] They are a useful tool to analyze electric and magnetic multipole radiation in wave guides [38][39][40][41][42] as well as to cope with anisotropy, bi-anisotropy and chiral isotropy [43][44][45][46]. Finally Hertz and Debye potentials intervene to tackle electromagnetism in General Relativity [23,40].…”