Covariant formulation of electrodynamics

Abstract

Abstract We now use the formalism developed in the previous chapter to rewrite Maxwell’s equations in a form that will make explicit their covariance under Lorentz transformation. We begin by showing that the charge and current density can be assembled into a four-vector, and we will then see how to write Maxwell’s equations in a covariant form. We then introduce the energy-momentum tensor of electromagnetic field and show how the conservation of energy and momentum can be written in terms of it. A more advanced section discusses the formulation of electrodynamics as a relativisitc field theory, the Lagrangian of the electromagnetic field, and the derivation of conservations laws from Noether’s theorem.