WS19 Quantum Field Theory

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

Prof. A. Weiler / Dr. W. Dybalski, WS 2019/20

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 10-12,Wed&Fri 10am-2pm, Thu 9:30-3:30pm. 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!


  • The repeat exam will take place in Garching in the tents on 24.9.2020 (Thursday morning). Please register on before the 13th of September. 
  • We will contact you once we hear back from the university about an exam date in mid to late September (20/8/20).
  • After getting your feedback concerning a repeat exam in June and the problems travel restrictions pose for some of you, we have decided to postpone it to mid-September.
  • The inspection of the first exam will happen once the situation has improved. Most likely it will be after April 19th, see here.
  • The second exam will have to be post-poned because of the SARS-CoV-2 Virus, see here and here.
  • 20.02: The results of the exercise bonus are available here
  • 28.1: The first exam will take place on Tuesday 11.02, from 9:00 to 12:00 in MW 1801, Ernst-Schmidt-Hörsaal (note this lecture hall is in the mechanical engineering building, see link). Please be there at 8:45. You can bring up to 4 pages (i.e. 2 two-sided A4 sheets) of handwritten notes and writing material, but no books or other notes. You will receive scratch paper from us. Please also bring your Student-ID card. If you intend to participate in the exam, please make sure that you are registered for it on TUMonline.
  • 22.1 Notice: For both groups 2 and 3 the tutorial of sheet 13 will be on 29.01, 4-6pm, in CH 26410.
  • 21.11 Notice: TMP students should hand-in the solution to the math problem 15 sheet 5, on 02.12, that is two days before it is discussed at the central tutorial on 04.12.
  • The first lecture will take place on the 14.10.
  • 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 also be provided (Dr. Dybalski).


Monday 12:00-13:30  (HS3)
Wednesday 12:15-13:45 (HS3)
and every alternating week: Wednesday 14.15-16.00 (HS3)

Central Tutorial

Every alternating week: Wednesday 14:15-16:00  (HS3)


Rooms and schedule:

group # time location tutor email
1 Mon 14:00 - 16:00 C.3202 Reuven B. reuven.balkin
- Wed 16:00 - 18:00 CH 26410 (backup room, no tutorial)  
2 Wed 16:00 -  18:00 PH II 227 Stefan S. stefan.stelzl
3 Thu 12:00 - 14:00 PH 1121 Max R. max.ruhdorfer

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:

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.

(Please contact for the password, it will be also announced during the lecture.)

QFT_script.pdf  (7/2/2020)

MathQFT_lecture_1.pdf (23/10/2019), 
MathQFT_lecture_2.pdf (18/11/2019), 
MathQFT_lecture_3.pdf (4/12/2019) 
MathQFT_lecture_4.pdf (18/12/2019)
MathQFT_lecture_5.pdf (29/1/2020)
MathQFT_lecture_6.pdf (29/1/2020)

Exercise Sheets

Exercise coordination: Dr. Javi Serra ( and Dr. Elena Venturini ( See sheet for hand-in requirements.


1st written exam: 11.02.2020, Ernst-Schmidt-Hörsaal (5508.01.801)

2nd written exam: 17.04.2020, Rudolf-Mößbauer-Hörsaal (5101.EG.501)

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. P. Vaudrevange.

P. Vaudrevange's script: part1.pdfpart2.pdf, and part3.pdf

Wed-Fri 9/10/11.10.2018: 10:00-11:30 and 12:30-14:00, PH II 127, Seminarraum E11

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