A derivation of Maxwell equations in quaternion space

Abstract

Quaternion space and its respective Quaternion Relativity (it also may be called as Rotational Relativity) have been defined in a number of papers including [1], and this new theory is capable to describe relativistic motion in elegant and straightforward way.
Nonetheless there are subsequent theoretical developments which remain an open question, for instance how to derive Maxwell equations in Q-space.
The purpose of the present paper is to derive a
consistent description of Maxwell equations in Q-space. First we consider a simplified method similar to the Feynman’s derivation of Maxwell equations from Lorentz force. And then we present another derivation method using Dirac decomposition, introduced by Gersten (1999). Further observation is of course recommended in order to refute or verify some implication of this proposition.