The course will last 6 lessons 2h each. It will start on 14th of May, from 14:00 to 16:00.
PREREQUISITES: basic special relativity (Lorentz transformations, time dilation, etc), classical electrodynamics (Maxwell equations, with potentials, covariant formulation of classical electrodynamics), quantum mechanics (state vector, operators, commutation relations), relativistic quantum mechanics (Dirac equation), Lagrangian formalism, quantum field theory.
CONTENTS:
Introductory Quantum Electrodynamics (QED)
Lecture I: Special relativity (reminder): four-vectors, Lorentz transformations, relativistic invariants. Electric and magnetic fields in moving frames, the need to introduce an electromagnetic tensor. The two relativistic invariants. Introduction to the Lagrangian formalism.
Lecture II: Discussion of the previous concepts, exercises. The Lagrangian of the scalar field. The Lagrangian of the classical electromagnetic field. The Euler-Lagrange equations of motion.
Lecture III: Historical introduction to quantum mechanics. Basic concepts. Dirac's equations. Solutions of the Dirac equation, spinors. The Dirac Lagrangian. Gauge invariance. The QED Lagrangian. (If time allows, maybe some discussion of the weak and strong interactions.)
Lecture IV: Discussion of the previous concepts, exercises. The quantum harmonic oscillator. Annihilation and creation operators. The quantization of the scalar field. The quantization of the Dirac field.
Lecture V: Feynman rules in QED. Elementary processes in QED.
Lecture VI: Feynman rules in QED (cont'd). E Calculation of the Klein-Nishina formula i. e. Compton scattering.
