Covariant formulation of classical electromagnetism

Summary

The covariant formulation writes classical electromagnetism in terms of tensors on Minkowski spacetime. The fields become the electromagnetic tensor, the potentials become the four-potential, and the sources become the four-current. In this form the laws look the same in every inertial frame, which makes their invariance under Lorentz transformations evident. It is also the starting point for electromagnetism in curved spacetime and for gauge theories.