## Quantum Field Theory

USOSThis 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 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:** After a majority vote, we decided together that the written exam for this course will take place on **Thursday, the 27th of June 2024, at 13:00** in **room 447** (the one where we also have our classes). It will take two hours and we will discuss a practice exam in the last tutorial to help you preparing for it. Please be there five minutes earlier such that we can start on time. Also 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, or, if you are in doubt, with me or Alex.

**Retake Exam:** As discussed via email, you have the chance to take part in the retake exam on **Friday, the 6th of September 2024, at 10:00** . Exactly the same conditions as described for the exam above will apply. If you would like to take part in the retake exam, please send me a quick message via email such that I have an estimated head count and can bring the right number of exams.

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 06:15, exercise
Reading: Peskin&Schroeder sections 7.5 and 10.1

- One-loop renoramlised $\phi^4$ theoryTutorial17.05.2024 06:15, exercise
Reading: [PeskSchr] section 10.2

- Renormalisation group flowTutorial24.05.2024 06:15, exercise
Reading: [PresSchr] section 12.1

- Gravity, quantum gravity, one-loop $\beta$-functions of a two-dimensional $\sigma$-model and string theoryLecture29.05.2024 08:15, notesTutorial06.06.2024 12:15, exercise
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 mechanismTutorial11.06.2024 12:15, exercise
Reading: [PresSchr] sections 11.1 and 20.1

There is no problem sheet for this lecture. In the tutorial, which takes place right before the last lecture, we discuss the practice exam. Moreover please note that Alex has be so kind to prepare extended notes on the renormalisation of the $\phi^4$ theory.

- BRST symmetry, physical Hilbert spaceLecture14.06.2024 15:00, notes
Reading: [PeskSchr] section 16.2-16.4