Quaternionic comparisons of electromagnetism using Lorentz transformations

Abstract

In this paper, by defining properties of the real and complex quaternion algebras, the electromagnetic field equations including monopoles have been studied in S ' reference systems, which moves with the velocity u according to the fixed reference system S. Quaternionic source and wave equalities have been derived in a more compact and elegant manner in S ' system. Besides, Poynting theorem has been firstly obtained in moving media. Additionally, the comparisons between S and S ' reference systems have been separately done for field, source, potential and wave equations in quaternion basis elements. Furthermore, Poynting theorems have been compared by means of S and S ' systems for the first time.