field equations, Eqs.(16)-(19), can be transformed into, $$\begin{aligned}
&& \blacktriangledown \cdot \textbf{B}^\prime = 0 ~,
\\
&& \partial_0 \textbf{B}^\prime + \blacktriangledown \times \textbf{E}^\prime / v_0 = 0 ~,
\\
&& \blacktriangledown \cdot \textbf{E}^\prime / v_0 = - \mu_e S_0   ~,
\\
&& \blacktriangledown \times \textbf{B}^\prime - \partial_0 \textbf{E}^\prime / v_0 = - \mu_e \textbf{S}^\prime ~,\end{aligned}$$ where $\textbf{B}^\prime = - \blacktriangledown \times \textbf{A}^\prime$, $\textbf{E}^\prime  / v_0 = \partial_0 \textbf{A}^\prime  + \blacktriangledown A_0$. $\textbf{A}^\prime  = \Sigma A_k \emph{\textbf{j}}_k$, $\textbf{S}^\prime  = \Sigma S_k \emph{\textbf{j}}_k$.

Expressing the above into the scalar equations will reveal that Eqs.(16)-(19) and Eqs.(28)-(31) are equivalent to each other. And the definition of Eq.(13) requires to substitute $\textbf{E}^\prime$ and $\textbf{B}^\prime$ by $\textbf{E}^{\prime\prime} = - \textbf{E}^\prime$ and $\textbf{B}^{\prime\prime} = - \textbf{B}^\prime¡ä$ respectively, in order to approximate to the Maxwell’s equations in the classical electromagnetic theory as near as possible. Therefore the electromagnetic field equations, Eqs.(28)-(31), are able to be transformed into that in the three-dimensional vector space, $$\begin{aligned}
&& \blacktriangledown \cdot \textbf{B}^{\prime\prime} = 0 ~,
\\
&& \partial_0 \textbf{B}^{\prime\prime} + \blacktriangledown \times \textbf{E}^{\prime\prime} / v_0 = 0 ~,
\\
&& \blacktriangledown \cdot \textbf{E}^{\prime\prime} / v_0 = \mu_e S_0   ~,
\\
&& \blacktriangledown \times \textbf{B}^{\prime\prime} - \partial_0 \textbf{E}^{\prime\prime} / v_0 = \mu_e 