Athanasios Chatzistavrakidis was awarded with NAWA's Ulam Fellowship and will join us for six month

Quantum Field Theory


One-loop contribution to the anomalous magnetic dipole moment 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

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: 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.

Additional material for the individual lectures, including the exercises which we discuss in the tutorials, is given below:

  1. Reminder of spin 0 and 1/2 fields
    Lecture23.02.2024 09:15, notes, show recording
    Tutorial23.02.2024 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.

  2. Reminder of spin 1 fields and abelian gauge symmetries
    Lecture01.03.2024 09:15, notes
    Tutorial01.03.2024 07:15, exercise

    Reading: [Ryder] sections 3.3 and 4.4

  3. Non-abelian gauge symmetries and Lie groups
    Lecture08.03.2024 09:15, notes
    Tutorial08.03.2024 07:15, exercise

    Reading: [PeskSchr] section 15 except for 15.3 or alternatively [Ryder] sections 3.5 and 3.6

  4. Path integral in quantum mechanics and for the scalar field
    Lecture15.03.2024 09:15, notes
    Tutorial15.03.2024 07:15, exercise

    Reading: [PeskSchr] section 9.1

  5. Generating functional, interactions and Feynman rules
    Tutorial22.03.2024 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.

  6. Path integral for fermions, Grassmann numbers, chiral anomaly (in the exercise)
    Lecture05.04.2024 08:15, notes, show recording
    Tutorial05.04.2024 07:15, exercise

    Reading: [PeskSchr] section 9.5

  7. Path integral for spin-1 bosons, ghost fields
    Lecture12.04.2024 08:15, notes, show recording
    Tutorial16.04.2024 06:15, exercise

    Reading: [PeskSchr] section 9.4

  8. One loop effects in QED: field-strength renormalisation and self-energy
    Lecture16.04.2024 08:15, notes, show recording
    Tutorial19.04.2024 06:15, exercise

    Reading: [PeskSchr] section 7.1

  9. Dimensional regularisation and superficial degree of divergence
    Lecture19.04.2024 08:15, notes, show recording
    Tutorial26.04.2024 06:15, exercise

    Reading: Peskin&Schroeder sections 7.5 and 10.1

  10. One-loop renoramlised ϕ4\phi^4 theory
    Lecture26.04.2024 08:15, notes, show recording
    Tutorial17.05.2024 06:15, exercise

    Reading: [PeskSchr] section 10.2

  11. Renormalisation group flow
    Lecture17.05.2024 08:15, notes, show recording
    Tutorial24.05.2024 06:15, exercise

    Reading: [PresSchr] section 12.1

  12. The Callan-Symanzik equation and β\beta-functions
    Lecture24.05.2024 08:15, notes
    Tutorial29.05.2024 06:15, exercise

    Reading: [PresSchr] sections 12.2

  13. Gravity, quantum gravity, one-loop β\beta-functions of a two-dimensional σ\sigma-model and string theory
    Lecture29.05.2024 08:15, notes
    Tutorial06.06.2024 12:15, exercise
  14. Spontaneous symmetry breaking and the Higgs mechanism
    Lecture06.06.2024 14:00, notes, practice exam, Alex's notes
    Tutorial11.06.2024 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 ϕ4\phi^4 theory.

  15. BRST symmetry, physical Hilbert space
    Lecture14.06.2024 15:00, notes

    Reading: [PeskSchr] section 16.2-16.4

Based on course 10, last update on June 12th 2024, 18:24:28 | Build 492 on June 19th 2024, 14:17:33 | Times and dates shown in UTC+00:00 | Contact