the principle of charge conservation expressed by the continuity equation (the basic axiom) and an heuristic handle of this equation which involved the principle of causality represented by the retarded time.

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The preceding axiomatic-heuristic approach can also be used to obtain the Maxwell equations in the four-dimensional Minkowski spacetime. Let us introduce the corresponding notation. A point is denoted by $x=x^{\mu}=\{x^0, x^i\}=\{ct, \textbf{x}\}$ and the signature of the metric is $(+,-,-,-).$ Greek indices run from 0 to 3 and Latin indices run from 1 to 3. The summation convention on repeated indices is adopted.

The continuity equation in the four-space is elegantly simple $$\begin{aligned}
\partial_\nu J^\nu =0,\end{aligned}$$ where $J^\nu$ is the four-current which is assumed to be a localised function of spacetime and $\partial_\mu$ is the four gradient. Our basic axiom is now represented by the covariant form of the continuity equation. A heuristic manipulation of this equation will lead us to the manifestly covariant form of Maxwell’s equations.

Our first task consists in finding a four-potential which is *causally* connected with the four-current via a covariant equation. The causal connection will be now implemented through the retarded Green function $G\!=\!G(x,x')$ for the four-dimensional wave equation: $\partial_\mu\partial^\mu G\!=\!\delta^{(4)}(x\!-\!x'),$ 