Maxwell Equations in Tensor Notation

[TheEtherWind]

²A^{[itex]\mu[/itex]}=-[itex]\mu[/itex]_oJ^{[itex]\mu[/itex]}

Griffith's Introduction to Electrodynamics refers to this 4-vector equation as "the most elegant (and the simplest) formulation of Maxwell's equations." But does this encapsulate the homogeneous Maxwell Equations? I see how the temporal components lead to Gauss' Law, and I'm assuming, though I haven't shown it to myself, that the spatial components lead to the Ampere-Maxwell Law. What about Faraday's Law and the divergence of B?

 

[Matterwave]

The other two laws are basically obtained by definition of the E and B fields. For example, by defining B as the curl of a vector potential, it is then divergence-less by definition.

I would say that the "most elegant" way to formulate Maxwell's equations is by using the Faraday tensor ([itex]F\equiv dA[/itex], where d is the exterior derivative) :

[tex]dF=0[/tex]

[tex]d*F=4\pi*J[/tex]

But this requires a little bit of differential geometry to understand.