Practical details about the course can be found in this note.
| Week | Section | Contents, roughly | ||
|---|---|---|---|---|
| 0 | ob, 2.1 | Introduction to quantum field theory (QFT). QFT as sum of special relativity and quantum mechanics. Lorentz symmetry as captured in index notation. Motivation for Klein-Gordon equation as 'quantization' of relativistic energy and momentum. | ||
| 1 | 2.2 & 2.3 | Classical mechanics in the Hamiltonian and Lagrangian forms. Noether's theorem. Canonical quantization. Particles and fields. | ||
| 2 | 2.4, 3.1, ob | Propagators: definition as correlation functions, interpretation as Green's functions. Advanced, retarded and Feynman type. More complicated relativistic wave equations: on-shell representations of Poincare algebra. | ||
| 3 | ob, 3.1-3.3 | Off-shell representations of Poincare algebra. Spinors, gamma matrices. Dirac equation and Lagrangian. Solutions to Dirac equation. | ||
| 4 | 3.4, 4.1 | Quantization of the Dirac field. Anti-commutation relations. Dirac propagator. Discrete symmetries. Towards perturbation theory: definition of interaction picture. Dyson's approach. | ||
| 5 | 4.1 - 4.3 | Dyson's approach. Time-ordered correlation functions. Perturbation theory. Wick's theorem. Feynman graphs as the graphical equivalent of Wick's theorem. Exponentiation of vacuum bubbles. | ||
| 6 | 4.3 - 4.7 | Cross-sections as a function of scattering amplitudes. Relation scattering amplitudes to Feynman graphs. Feynman rules for fermions. Yukawa theory. | ||
| 7 | 4.8 - parts of section 5 | Quantum Electrodynamics: Lagrangian, Feynman rules, first physical cross-sections | ||
| 8 | parts of 7.5 | Dimensional regularization | ||
| 9 | 6.1 - parts of 6.2 | My first loop calculation: Electron vertex. Form factors and their physical interpretation. Calculation of anomalous magnetic moment. | ||
| 10 | 6.3 - 6.4 | Electron vertex, evaluation. Divergent structure in ultraviolet and infrared. Cancellation of divergences. | ||
| 11 | 7.1 - 7.2 | Kahlen-Lehmann spectral representation. Self energy graphs | ||
| 12 | 7.3 - 7.4 | LSZ reduction. Connection between correlation functions and scattering amplitudes. The Ward identity. | ||
| 13 | 7.5 | Self energy of the photon. Vacuum polarization. |