What is Four-potential and field tensor?

The potentials of the Year 2 volume assemble into the four-potential

and the measurable fields $\vect E = -\vect\nabla V - \partial_t\vect A$, $\vect B = \operatorname{\vect{curl}}\vect A$ are the six independent components of one antisymmetric array, the electromagnetic field tensor

$\vect E$ and $\vect B$ are not two fields but six faces of one object; which face an observer calls “electric” depends on the observer’s motion.