Quantum Field Theory
USOS
This is the mandatory Quantum Field Theory course of the Master in Theoretical Physics at the University of Wrocław. It is tailored towards master and PhD students who are familiar with
- quantum mechanics
- electrodynamics
- special relativity
- quantum electrodynamics.
There are many good books on the subject, four that I like are
- [PeskSchr] Peskin, Schroeder: An introduction to quantum field theory
- [Ryder] Ryder: Quantum Field Theory
- Weinberg: The Quantum Theory of Fields, Volume 1 & 2
- Zee: Quantum Field Theory in a Nutshell.
We will follow mostly the first one in the lectures. There will be 2 hours of lectures and 2 hours of tutorial each week. Exercises will be posted here a week before the tutorial they are discussed in. Please keep in mind that active participation in the tutorials is important to pass the course. Prof. Pok Man Lo will be in charge of the tutorials with M.Sc. Alex Swash as assistant. Please fell free to contact them or me if you have any questions. For information about credits points, please refer to the syllabus (in Polish) or contact me directly.
Important: Students will be assigned to exercise problems by the system described here at the Monday, 9:00 pm, before the tutorial. Please indicate your preferences by then.
Exam: will be in written at the end of the semester. Please note that you need to have more than 50% of the points from the exercises assigned to you to qualify for the exam. You can check your points here on the website.
Additional material for the individual lectures, including the exercises which we discuss in the tutorials, is given below:
- Reminder of spin 0 and 1/2 fieldsTutorial23.02.2024 07:15, exercise
Reading: [PeskSchr] sections one and two
Please note that there are no exercise assignments for the first seminar. Instead, we continue with the lecture.
- Generating functional, interactions and Feynman rulesTutorial22.03.2024 07:15, exercise
Reading: [PeskSchr] section 9.2
From here on, we will often expand the path integral using a perturbation parameter, like a coupling strength. The resulting power series can be elegantly organized in terms of Feynman diagrams. Because of the importance, I would like to show you all the step of this computation which is to long for the lecture. Therefore, we will use the last 40 minutes of the tutorial to discuss how Feynman diagrams and symmetry factors explicitly arise from the path integral. Above you will also find a copy of the computation for your reference.
- Path integral for fermions, Grassmann numbers, chiral anomaly (in the exercise)Tutorial05.04.2024 07:15, exercise
Reading: [PeskSchr] section 9.5
- Path integral for spin-1 bosons, ghost fieldsTutorial16.04.2024 06:15, exercise
Reading: [PeskSchr] section 9.4
- One loop effects in QED: field-strength renormalisation and self-energyTutorial19.04.2024 06:15, exercise
Reading: [PeskSchr] section 7.1
- Dimensional regularisation and superficial degree of divergenceTutorial26.04.2024 07:15, exercise
Reading: Peskin&Schroeder sections 7.5 and 10.1
- Renormalisation group flowLecture17.05.2024 08:15
Reading: [PresSchr] section 12.1
- The Callan-Symanzik equation and -functionsLecture24.05.2024 08:15
Reading: [PresSchr] sections 12.2
- Gravity, quantum gravity, one-loop -functions of a two-dimensional -model and string theoryLecture29.05.2024 08:15
Reading: David Tong's lecture notes on String Theory section 7.1, original article Phys.Rev.Lett. 45 (1980) 1057
- Spontaneous symmetry breaking and the Higgs mechanismLecture07.06.2024 08:15
Reading: [PresSchr] sections 11.1 and 20.1
There is no problem sheet for this lecture. In the tutorial, which takes place right after the last lecture, we discuss the practise exam.
- BRST symmetry, physical Hilbert spaceLecture14.06.2024 15:00
Reading: [PeskSchr] section 16.2-16.4