Lecturer
Begin of lecture
Wednesday, 13. April 2022
Time & Place
- Wednesday, 08:00 - 09:30, Seminar Room 5.331, Pfaffenwaldring 57
- Friday, 09:45 - 11:15, 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
This course follows the exposition of Peskin & Schroeder.
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
Requirements
The concept of second quantization is necessary to understand the quantization of fields. If you did not learn about second quantization in your advanced quantum mechanics course, I suggest that you catch up by self-study (any textbook on advanced quantum mechanics covers this topic). The same goes for the basic concepts of special relativity.
In particular, you should be familiar with the following concepts:
- Creation and annihilation operators
- Bosonic and fermionic (anti)commutation relations
- Constructing the bosonic/fermionic Fock space from the vacuum state (number states)
- Basics of special relativity: Lorentz group, Minkowski metric, Lorentz scalars and four-vectors ...
Knowledge of relativistic quantum mechanics it not required; however, it is certainly helpful if you have seen the Klein-Gordon and Dirac equation before. I will briefly rederive the Dirac equation from a "field theory" point of view.
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 (planned, may be subject to changes) |
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1 | 13.04.22 | - Lagrangian and Hamiltonian formalism - Symmetries |
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2 | 20.04.22 | - Noether's theorem - Energy-momentum tensor |
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3 | 22.04.22 | - Quantization of the Klein-Gordon field - The Klein-Gordon field in spacetime |
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4 | 27.04.22 | - Causality of the Klein-Gordon field - Feynman propagator of the Klein-Gordon field |
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5 | 29.04.22 | - The Dirac equation - Free-particle solutions of the Dirac equation |
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6 | 04.05.22 | - Dirac field bilinears - Quantization of the Dirac field |
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7 | 06.05.22 | - Spin and statistics - The Dirac propagator - Causality - Discrete symmetries of the Dirac theory |
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8 | 11.05.22 | - Interacting QFTs - Perturbation expansion of correlation functions - Wick's theorem |
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9 | 13.05.22 | - Feynman diagrams - Feynman rules |
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10 | 18.05.22 | - Disconnected Feynman diagrams - Vacuum energy - Scattering cross sections |
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11 | 20.05.22 | - S- and T-matrix | |
12 | 25.05.22 | - S-matrix elements from Feynman diagrams - Feynman rules for scattering amplitudes |
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13 | 27.05.22 | - Wick's theorem for fermions - The photon propagator - Feynman rules for quantum electrodynamics |
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14 | 01.06.22 | - Electron-electron scattering - Electron-positron scattering - The muon-antimuon production cross section |
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15 | 03.06.22 | - Overview of radiative corrections - Soft bremsstrahlung - Formal structure of the electron vertex function |
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16 | 15.06.22 | - The Landé g-factor - Evaluation of the vertex integral |
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17 | 17.06.22 | - Evaluation of the vertex integral (continued) | |
18 | 22.06.22 | - Infrared divergence of the vertex function - Källén–Lehmann spectral representation |
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19 | 24.06.22 | - Field-strength renormalization - Physical mass vs. bare mass |
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20 | 29.06.22 | - Electric charge renormalization - Dimensional regularization |
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21 | 01.07.22 | - Vacuum polarization - Lamb shift - Running of the fine-structure constant - Landau pole and Dyson's argument |
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22 | 06.07.22 | - Systematics of UV-divergences - Mass dimension and renormalizability - Note on quantum gravity |
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23 | 08.07.22 | - Bare perturbation theory - Renormalized perturbation theory for Phi-4-theory |
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24 | 13.07.22 | - The path integral in quantum mechanics - Derivation of the Schrödinger equation - The path integral for fields |
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25 | 15.07.22 | - Correlation functions from path integrals - Faddeev-Popov gauge-fixing procedure - Photon propagator |
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26 | 20.07.22 | - Structure of the QED U(1) gauge symmetry - Generalization to non-abelian gauge groups (1) |
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27 | 22.07.22 | - Generalization to non-abelian gauge groups (2) - Yang-Mills Lagrangian - Higgs mechanism for U(1) gauge theory (1) - Goldstone theorem |
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28 (Bonus) | 27.07.22 | - Higgs mechanism for U(1) gauge theory (2) - Structure of the Standard Model |
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29 (Bonus) | 29.07.22 | - Glashow-Weinberg-Salam Theory - Higgs mechanism in the Standard Model (1) |
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30 (Bonus) | 03.08.22 | - Higgs mechanism in the Standard Model (2) - Quantum Chromodynamics - Summary |
You can also download a combined PDF including all blackboard notes of this course.
Problem Sets
No. | Published | Due | Download | Comments |
---|---|---|---|---|
1 | 13.04.22 | 22.04.22 | ||
2 | 22.04.22 | 29.04.22 | ||
3 | 29.04.22 | 06.05.22 | ||
4 | 06.05.22 | 13.05.22 | ||
5 | 13.05.22 | 20.05.22 | ||
6 | 20.05.22 | 27.05.22 | ||
7 | 27.05.22 | 03.06.22 | ||
8 | 03.06.22 | 17.06.22 | ||
9 | 17.06.22 | 24.06.22 | ||
10 | 24.06.22 | 01.07.22 | ||
11 | 01.07.22 | 08.07.22 | ||
12 | 08.07.22 | 15.07.22 | ||
13 | 15.07.22 | 22.07.22 |
Tutorials
Tutor | Room | Day | Time |
---|---|---|---|
Nastasia Makki | 4.331 | Friday | 11:30 - 13:00 |