This is an advanced course in special relativity and electrodynamics, aimed to provide a thoughtful introduction to the subject at the level of a beginning graduate student. The level of physical and mathematical sophistication is quite high. Differential forms and advanced calculus are thoroghly used without apology. The objective is that the student can appreciate the nature and character of special relativity and how this theory fits into the general scheme of modern Physics.

Program:
Introduction to relativity, an overview. Deduction of the Lorentz transformations and their properties. Connecion with group theory. The  role of the speed of light. The Lorentz group and the Poincaré group. Spinorial representation. The universal covering of the Lorentz group: Sl(2,C). Topological properties. Minkowski vector spaces and Minkowski spacetime. Timelike, spacelike, nulllike 4-vectors. The light-cone. Meaning of spacetime separation between events. Causality in Minkowski spacetime: Cronological and causal past and future of an event. Acronal sets. Tensor algebra over a Minkowskian vector space. Vector bundles over Minkowski spacetime. Tensor fields. Differental forms and their properties. Exterior derivative, integration, Stokes theorem and codifferential. Manifestly covariant formulation of electromagnetism: the Faraday 2-form. Examples. Gauge invariance and the 4-potential. The Lorenz gauge. Gauge invariant quantities and topology. The wave equation and retarded Green functions. The Lorentz force and the energy-momentum tensor of the electromagnetic field. Variational deduction of Maxwell equations in manifestly covariant form. Introduction to field theory on Minkowski spacetime. Relativistic kinematics and dynamics. Proper time, 4-velocity and 4-acceleration. Local inertial frames. Proper mass. 4-forces in special relativity. Heat type forces. Conservation laws. Relativistc particle mechanics. 4-momentum conservation and its meaning. Equivalence of energy and mass. Compton and inverse-compton effect. Threshold energies for subnuclear reaction. Inclusive and exclusive processes and their relativistic kinematics. The center of momentum frame.     Examples.

Prerequisites:
Introductory courses in Mechanics and Electrodynamics, Calculus. Advanced topics in tensorial analysis, topology, and differential geometry will be introduced during the lectures.