Electrodynamics: Gauge Invariance and Electrostatics

This lecture covers the concepts of gauge invariance and electrostatics, including the Lorenz gauge, Poisson equation, and Dirac delta-function. It delves into Maxwell's equations, electromagnetic waves, and the speed of propagation. The instructor explains the importance of gauge invariance in solving wave equations and introduces the Lorenz gauge, leading to the derivation of wave equations. Furthermore, the lecture explores electrostatics, focusing on finding solutions that satisfy the Poisson equation. General boundary conditions, such as Dirichlet and Neumann boundary conditions, are discussed, emphasizing the uniqueness of the solution.