Relativistic Electrodynamics

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Electrodynamics is the first example of a field theory: charged particles create a field and this field acts on other charged particles. In other words electromagnetic forces are mediated by a field. This should put in contrast to Coulomb’s law in electrostatics or even Newton’s gravitational law. Both laws imply the objectionable notion of an action on a distance: moving a charge or mass at location A instantaneously gives rise to a different force at point B. How the electromagnetic field evolves in time is given by the 4 famous Maxwell equations. These equations for example state that light propagates at a constant speed, which eventually led to Einstein’s theory of relativity. Electrodynamics is thus by construction a relativistic theory. This course will start at the Maxwell equations and their consequences: conservation laws, electromagnetic waves, radiation, etc… I will introduce the magnetic vector potential. We have a certain freedom in defining this vector potential, this freedom is more formally called "gauge invariance", an important concept in understanding any field theory. Evidently, I will also discuss the tight relation between electrodynamics and relativity and explain for example how magnetism can be understood as relativistic electric force.