Relativistic Electrodynamics

The concept of action is introduced using Lagrangian and Hamiltonian mechanics, and is used to describe the relativistic mechanics of a free particle: free particle canonical 4-momentum and angular momentum 4-tensor. The problem of a charged particle in an external field is considered in detail, resulting in the relativistic version of the Lorentz force law. The electromagnetic field is described using the action principle: The Lagrange density function and the recovery of Maxwell’s equations and charge conservation. The simplest Lagrangian density that can be constructed from a four-vector field is known as the “proca Lagrangian,” but it is shown to predict a massive photon. Finally, the canonical stress-energy tensor is derived along with conservation laws.