I. Relativistic quantum mechanics
Tensor notation. Casimir operators. The Poincaré group. Irreducible representations of particles. The Klein-Gordon equation. The Dirac equation. The structure of Dirac particles. The Dirac equation: central potentials. The Weyl equation. Maxwell's equations and quantization of the electromagnetic field. Introduction to Yang-Mills theory.
II. Introduction to quantum field theory
Neutral and charged Klein-Gordon fields. The Dirac field. The Majorana field. Asymptotic fields: LSZ formulation. Perturbation theory. Introduction to quantum electrodynamics. Interacting fields and Feynman diagrams. Elementary processes of quantum electrodynamics. Introduction to radiative corrections.
After completed course, the PhD student should be able to:
- apply the Poincaré group as well as classify particle representations.
- analyze the Klein-Gordon and the Dirac equations.
- solve the Weyl equation.
- know Maxwell's equations and classical Yang-Mills theory.
- quantize Klein-Gordon, Dirac, and Majorana fields as well as formulate the Lagrangian for these fields.
- use perturbation theory in simple quantum field theories.
- formulate the Lagrangian for quantum electrodynamics as well as analyze this.
- derive Feynman rules from simple quantum field theories as well as interpret Feynman diagrams.
- analyze elementary processes in quantum electrodynamics.
- compute radiative corrections to elementary processes in quantum electrodynamics.
