Reformulation of electromagnetism with octonions

Abstract

In this paper, the octonion algebra and its general properties are defined by two different multiplication rules for octonion units. The field equations, potential and Maxwell equations for electromagnetism are investigated with new octonionic equations and these equations are cornpared with their vectorial representations. Also, the potential and wave equations for fields without sources are given. Then, Maxwell equations are considered for magnetic monopole and free space.