Quaternion in electrodynamics
I recently listened to a public lecture on the electrodynamics at the middle night on New Year's Eve. This is the first time I heard that the Maxwell equation is initially described by James Clerk Maxwell himself with the help of quaternion , a mathematics created by Sir William Rowan Hamilton in 1843. But in today's textbooks, Maxwell equations are taught in the language of vector analysis and the concept of quaternion has been completely eliminated. A brief review of this history, for example, can be found in the paper "Development of Vector Analysis from Quaternions" . Quaternion definition As the generalization of the complex number $z=a+i\,b$ with $i^2=-1$, quaternion is defined in the form of \begin{equation} \mathcal{Q} = q_0+q_1\,\mathbf{i}+q_2\,\mathbf{j}+q_3\,\mathbf{k}\,\tag{1}\end{equation} where $q_0, q_1, q_2,q_3\in \mathbb{R}$ and $\mathbf{i}, \mathbf{j},\mathbf{k}$ satisfy the multiplication rule \begin{equation}\mathbf{i}^2=\mathbf{j}^2=\mathbf{k