Important
Lecturer
Begin of lecture
8. April 2020
Time and Date
- Wednesday, 08:00 - 09:30, Seminar Room 5.331, Pfaffenwaldring 57
- Friday, 14:00 - 15:30, Seminar Room 5.331, Pfaffenwaldring 57
General Information
- The lecture and the tutorials will be given in English.
- There are two types of exercises: "Written" exercises are handed in in class and graded/corrected by the tutor. "Oral" exercises are discussed in the tutorials and presented by students on the blackboard.
- Admission to the final exam requires 80% of the written scores, 66% of the oral scores, and presenting a problem on the blackboard twice.
- Please register for the exercise groups online. To do so, you need the Lecture Key given in the first lecture.
- If you assign a password at the registration, you can request your current scores here.
Examination
There will be an oral examination at the end of the course. Details will be given in the lecture.
Literature
- Weinberg: The Quantum Theory of Fields (Volume 1)
Standard reference, very rigorous & mathematical, ratio #formulas/#text = high - Itzykson/Zuber: Quantum Field Theory
Standard reference, ratio #formulas/#text = high - Peskin/Schroeder: An Introduction to Quantum Field Theory
Standard reference for courses on QFT, ratio #formulas/#text = medium - Zee: Quantum Field Theory in a Nutshell
Compact and pedagogical introduction to the field, #formulas/#text = low
Topics
The goal is to gain a thorough understanding of relativistic quantum field theory, the concepts of Feynman diagrams, renormalisation for quantum electrodynamics, and to extend this knowledge to non-abelian gauge theories. In particular:
- Relativistic quantum mechanics and Dirac equation
- Path integral formalism
- Quantisation - Free fields
- Interacting fields and Feynman diagrams
- Elementary processes and first corrections
- Renormalisation
- Non-abelian gauge fields
Script
These notes follow mostly the exposition of Peskin & Schroeder. They are not an extension of the material covered in the lectures but the script that I use to prepare them. Please have a look at Peskin & Schroeder and the given references for more comprehensive coverage; the corresponding pages are noted in the headers (→ P&S • pp. xx-yy).
Lectures
| No. | Date | Notes | Topics |
|---|---|---|---|
| 1 | 08.04.2020 | - Lagrangian and Hamiltonian formalism - Symmetries |
|
| 2 | 15.04.2020 | - Noether's theorem - Energy-momentum tensor |
|
| 3 | 17.04.2020 | - Quantization of the Klein-Gordon field - The Klein-Gordon field in spacetime |
|
| 4 | 22.04.2020 | - Causality of the Klein-Gordon field - Feynman propagator of the Klein-Gordon field |
|
| 5 | 24.04.2020 | - Notes on the Poincaré group - The Dirac equation - Free-particle solutions of the Dirac equation |
|
| 6 | 29.04.2020 | - Dirac field bilinears - Quantization of the Dirac field |
|
| 7 | 06.05.2020 | - Spin and statistics - The Dirac propagator - Causality - Discrete symmetries of the Dirac theory |
|
| 8 | 08.05.2020 | - Interacting QFTs - Perturbation expansion of correlation functions - Wick's theorem |
|
| 9 | 13.05.2020 | - Feynman diagrams - Feynman rules |
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| 10 | 15.05.2020 | - Disconnected Feynman diagrams - Vacuum energy |
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| 11 | 20.05.2020 | - Scattering cross sections - S- and T-matrix |
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| 12 | 22.05.2020 | - S-matrix elements from Feynman diagrams - Feynman rules for scattering amplitudes |
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| 13 | 27.05.2020 | - Wick's theorem for fermions - The photon propagator - Feynman rules for quantum electrodynamics |
|
| 14 | 29.05.2020 | - Electron-electron scattering - Electron-positron scattering - The muon-antimuon production cross section |
|
| 15 | 10.06.2020 | - Overview of radiative corrections - Soft bremsstrahlung - Formal structure of the electron vertex function |
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| 16 | 12.06.2020 | - The Landé g-factor - Evaluation of the vertex integral |
|
| 17 | 17.06.2020 | - Infrared divergences in first order - Cancellation in arbitrary order - The Sudakov form factor |
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| 18 | 19.06.2020 | - Källén–Lehmann spectral representation - Field-strength renormalization - Physical mass vs. bare mass |
|
| 19 | 24.06.2020 | - Electric charge renormalization - Dimensional regularization - Vacuum polarization |
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| 20 | 26.06.2020 | - Systematics of UV-divergences - Mass dimension and renormalizability - Note on quantum gravity |
|
| 21 | 01.07.2020 | - Bare perturbation theory - Renormalized perturbation theory for Phi-4-theory and QED |
|
| 22 | 03.07.2020 | - The path integral in quantum mechanics - Derivation of the Schrödinger equation - Correlation functions from path integrals for fields |
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| 23 | 08.07.2020 | - Faddeev-Popov gauge-fixing procedure - Photon propagator |
|
| 25 | 10.07.2020 | - Structure of the QED U(1) gauge symmetry - Generalization to non-abelian gauge groups - Yang-Mills Lagrangian |
|
| 25 | 15.07.2020 | - Higgs mechanism for an abelian U(1) gauge theory - Goldstone theorem - Gauge-invariant formulation |
|
| 26 | 17.07.2020 | - Glashow-Weinberg-Salam Theory - Higgs mechanism and mass generation - Quantum Chromodynamics |
Problem Sets
| No. | Problem Set | Date | Comments |
|---|---|---|---|
| 1 | Problem Set 01 | 08.04.2020 | to be handed in via ILIAS until Friday, April 17 (recommended) or until the end of the lecture period (mandatory) |
| 2 | Problem Set 02 | 17.04.2020 | |
| 3 | Problem Set 03 | 24.04.2020 | |
| 4 | Problem Set 04 | 01.05.2020 | |
| 5 | Problem Set 05 | 08.05.2020 | |
| 6 | Problem Set 06 | 15.05.2020 | |
| 7 | Problem Set 07 | 22.05.2020 | |
| 8 | Problem Set 08 | 29.05.2020 | |
| 9 | Problem Set 09 | 12.06.2020 | |
| 10 | Problem Set 10 | 19.06.2020 | |
| 11 | Problem Set 11 | 26.06.2020 | |
| 12 | Problem Set 12 | 03.07.2020 | |
| 13 | Problem Set 13 | 10.07.2020 |
Tutorials
| Tutor | Room | Day | Time |
|---|---|---|---|
| Jan Kumlin / Nastasia Makki | 5.331 | Friday | 11:30 - 13:00 |