to those given in the section 3 for the case of electromagnetic expressions in SI units. If $\mathscr{C}=c$ then ${\cal G}=G$. If in this case we make ${\cal J}^\nu= J^\nu$ and ${\cal A}^\nu= A^\nu/\mu_0$ with $A^\nu=(\Phi/c,\mathbf{A})$ then (44) becomes (23) and $A^\nu$ is the electromagnetic four-potential in SI units.

It is possible consider a different heuristic handle of the continuity equation (the basic axiom) to formulate a theorem that is equivalent to the previously considered existence theorem. For example, we can formulate the following existence theorem [@6]: Given the localised sources $\rho(\textbf{x},t)$ and $\textbf{J}(\v x,t)$ satisfying the continuity equation $\nabla\cdot \textbf{J}+\partial\rho/\partial t=0$ there exist the retarded fields $\textbf{F}(\textbf{x},t)$ and $ \textbf{G}(\textbf{x},t)$ defined by $$\begin{aligned}
 \textbf{F} =
 \frac{\alpha}{4\pi}\int\bigg(\frac{\hat{\textbf{R}}}{R^2}[\rho]+\frac{\hat{\textbf{R}}}{Rc}\left[\frac{\partial \rho}{\partial t}\right]
-\frac{1}{Rc^2}\left[\frac{\partial \textbf{J}}{\partial t}\right]\bigg)\, d^3x',\\
 \textbf{G}=
 \frac{\beta}{4\pi}\int \bigg([\textbf{J}]\times\frac{\hat{\textbf{R}}}{R^2 }+\bigg[\frac{\partial \v J}{\partial t}\bigg]\times\frac{\hat{\textbf{R}}}{R c}\bigg)\, d^3x'.\end{aligned}$$ that satisfy the following field equations: $\nabla\cdot \textbf{F}=\alpha\rho,\,\nabla\cdot \textbf{G}=0,\,
 \nabla\times\textbf{F}+\chi \partial \textbf{G}/\partial t=0$ and $
\nabla\times \textbf{G}-(\beta/\alpha)\partial \textbf{F}/\partial t
=\beta \textbf{J}.$ Here $\hat{\textbf{R}}={\textbf{R}}/R =(\textbf{x}-\textbf{x}')/|\textbf{x}- \textbf{x}'|$ and equations (45) and (46) are in the $``\alpha\beta\chi$” system defined by $\alpha=\beta\chi c^2$. In this case the axiomatic-heuristic approach shows the existence of the electric and magnetic fields in the generalized form of Coulomb and Biot-Savart laws given by Jefimenko [@6] which 