WS21 Quantum Field Theory

(Physics Master Course TUM; TMP core module LMU/TUM)

Prof. A. Weiler, WS 2021/22

The lecture is aimed at master students with an interest in theoretical physics. It is a crucial preparation for a master thesis in theoretical particle physics. The quantum field theory concepts discussed are however more widely applicable. The focus here will be on methods, rather than on phenomenology (as compared to the 'Theoretical particle physics' course).

Preparatory course Oct 12-14,Tue-Thu 10am-4pm, Strongly advised for students who have not attended the "Relativity, Particles, Fields'' course at TUM in the summer or wish to refresh their theoretical physics background. More information at Preparatory Course below.

Please register for the lecture on, especially if you are a TMP TUM/LMU student.

We have created a moodle page where you can also find a link to register for our Slack workspace. LMU students can be manually added to the moodle page -- please contact me via email.


  • NEW lecture hall and different time on Monday due to space constraints
  • The first lecture will take place on 18.10.2021
  • The slot on Wednesday 2:15-4pm will be used for the central tutorial and additional lectures.


  • Lagrange formalism and canonical quantisation of the scalar field
  • Path integral representation of quantum field theory
  • Green functions and scattering processes
  • Regularization and renormalization
  • Effective quantum field theory and the computation of quantum loop corrections
  • Renormalization group
  • Symmetries and relativistic particles and quantum fields with spin
  • Spinors
  • Massless spin 1 fields and gauge redundancy

Insights into mathematical foundations of QFT will be provided by Dr. Maximilian Duell.


Monday 10:00-12:00  (LMU Lecture Hall Garching)
Wednesday 12:15-13:45 (LMU Lecture Hall Garching)
and every alternating week: Wednesday 14.15-16.00 (LMU Lecture Hall Garching)

Central Tutorial

Every alternating week: Wednesday 14:15-16:00  (LMU Lecture Hall Garching)


Rooms and schedule: 

group # time location tutor email
1 Mon 14:00 - 16:00 PH 1121 XX XX
- Mon 16:00 - 18:00 CH 26410 (backup room, no tutorial)  
2 Wed 16:00 -  18:00 PH II 227 XX XX
3 Thu 12:00 - 14:00 PH 1121 XX XX

If obtained, the exercise bonus of 0.3 points is valid for the first attempt at the final exam. It only applies to a passed exam, in particular 4.3 is not upgraded to 4.0.


It is very helpful to have heard a course similar to Relativity, Particles, Fields at TUM. Please study the parts Prof. Weiler's Relativity, Particles, Fields script.pdf which haven't been covered in your previous lectures.

See also information about the preparatory course below. 

Note that the RPF script uses slightly different conventions, e.g. annihilation and creation operators aRPF -> (2 E_p)1/2 aQFT and particle states: |p>RPF -> (2 E_p)1/2 |p>QFT which affects the form of the expansion of Φ(x) etc.


We will not follow a single book but it is strongly recommended that you read up on the topics discussed in the lecture in one or more of these books:

Schwartz - Quantum Field Theory and the Standard Model (recommended).

Note that Schwartz uses slightly different conventions, e.g. annihilation and creation operators  aschwartz -> (2 E_p)1/2 aweiler and particle states: |p>schwartz -> (2 E_p)1/2 |p>weiler which affects the form of the expansion of Φ(x) etc.)

S. Weinberg - Quantum Field Theory (1 & 2)     
Peskin/Schroeder - An Introduction to Quantum Field Theory
Preskill - Lecture notes (on his Caltech website)
Cheng/Li - Gauge theory of elementary particle physics

and for the more mathematically oriented:

Jonathan Dimock - Quantum Mechanics and Quantum Field Theory, A Mathematical Primer
R. Haag - Local Quantum Physics, Fields, Particles, Algebras, Springer
J. Glimm/A. Jaffe - Quantum Physics, A Functional Integral Point of View, Springer

Sign conventions across QFT books, see here

Lecture Notes

Please only use the latest version of these notes, since we are constantly fixing typos and improving the presentation. Many of you use a printed version of the first latex draft, which had a lot of transcription errors.

See moodle page.


Exercise Sheets

Exercise coordination: Dr. Pietro Baratella, Dr. Javi Serra, and Dr. Elena Venturini. You can hand in the exercises on the moodle page. If you have questions about the exercises please use the Slack channel (link on moodle page).

Exercise bonus: in order to obtain the -0.3 bonus (applicable to the first exam attempt, and only to passing grades) you will need to attend regularly the tutorials, present/discuss the solution of at least one exercise, and hand in solutions for at least 50% of the total number of exercises.


1st written exam: Fr 04.03.2022, 11:30 - 14:30

2nd written exam: Mo 11.04.2022, 11:30 - 14:30

Preparatory Course

The preparatory course will review some basic concepts from the theory of continuous systems and advanced quantum mechanics to facilitate students with various backgrounds to deal with the rapid start of the course. Highly recommended.

Topics: Action principle in classical mechanics, Euler-Lagrange equations for continuous systems (vibrating string) and classical fields, quantization, Fock space, ...

The preparatory course will be taught by Dr. Javi Serra in HS2 in the Physics Department in Garching. 

  1. Tue 12.10.  10-12, 14-16
  2. Wed 13.10.  9-11,  11-13
  3. Thu 14.10.  10-12, 14-16

You can also consult Prof. Weiler's Relativity, particles, fields script which covers similar topics.