Quantum Field Theory
Module version of WS 2017/8
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
|available module versions|
|WS 2019/20||WS 2018/9||WS 2017/8||WS 2016/7||WS 2015/6||WS 2013/4||WS 2010/1|
PH2041 is a semester module in English or German language at Master’s level which is offered in winter semester.
This Module is included in the following catalogues within the study programs in physics.
- Theory courses for nuclear, particle, and astrophysics
- Complementary catalogue of special courses for condensed matter physics
- Complementary catalogue of special courses for Biophysics
- Complementary catalogue of special courses for Applied and Engineering Physics
- Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
If not stated otherwise for export to a non-physics program the student workload is given in the following table.
|Total workload||Contact hours||Credits (ECTS)|
|300 h||105 h||10 CP|
Responsible coordinator of the module PH2041 in the version of WS 2017/8 was Martin Beneke.
Content, Learning Outcome and Preconditions
- Basic Concepts of Quantum Field Theory
- Path integral representation of quantum field theory, perturbation expansion, Feynman diagrams
- From Green functions to scattering cross sections, particle states, LSZ reduction
- Renormalization, regularization, effective field theory, renormalization group, running couplings
- Symmetries and relativistic particles & quantum fields with spin, fermionic path integral, Feynman rules for general fields
- Vector fields and gauge symmetry, quantum electrodynamics
After successful completion of the module the students are able to
- to compute Green functions in perturbation theory, including loop corrections, and apply these to calculations of high-energy reactions;
- to quantise non-Abelian gauge theory and to calculate tree- and loop processes;
- to understand the concepts of regularisation and renormalisation and to apply these in calculations;
- to improve perturbative calculations using the renormalisation group;
- to construct effective quantum field theories.
No preconditions in addition to the requirements for the Master’s program in Physics. Very helpful is an introductory lecture like “Relativity, particles, fields”.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
|VO||5||Quantum Field Theory||Beneke, M. Dybalski, W.||
Mon, 12:00–14:00, PH HS3
Wed, 12:00–14:00, PH HS3
Wed, 14:00–16:00, PH HS3
|UE||1||Exercise to Quantum Field Theory||
Responsible/Coordination: Beneke, M.
|dates in groups|
|UE||1||Large Exercise to Quantum Field Theory||
Responsible/Coordination: Beneke, M.
Wed, 14:00–16:00, PH HS3
Learning and Teaching Methods
Lecture, blackboard presentation; homework problems and their discussion in tutorial groups
The lecture is designed for the presentation of the subject, usually by blackboard presentation. The focus resides on theoretical foundations of the field, presentation of methods and simple, illustrative examples. Command of basic methods is deepened and practised through homework problems, which cover important aspects of the field. The homework problems should develop the analytic skills of the students and their ability to perform calculations. The homework problems are discussed by the students themselves under the supervision of a tutor in order to develop the skills to solve and explain a physics problem coherently.
Blackboard, possibly supplemented with slides. Homework problems for deepening and practising the learned topics
- Peskin & Schroeder, "An Introduction to Quantum Field Theory"
- Weinberg, "Quantum Theory of Fields"
- Schwartz, "Quantum Field Theory and the Standard Model"
Description of exams and course work
There will be a written exam of 180 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.
For example an assignment in the exam might be:
- Calculate the Feynmanrules of a QFT with Scalar, Fermion or Vector fields and determine the leading contribution to the scattering cross-section of a 2->2 process.
- Calculate a 1-loop diagram, regularize and renormalize
- Integrate out a heavy particle and determine the resulting effective field theory
- Determine the Noether-current and the Ward Identities of a QFT with scalar fields in the fundamental of SO(3)
- Calculate the beta function and determine its behavior.
Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.
There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of
- 1. preparing at least 50% of the exercises on the exercise sheets,
- 2. presenting at least three exercises at the blackboard,
- 3. participtating actively in the tutorials.
The exam may be repeated at the end of the semester.
Current exam dates
Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.
|Exam to Quantum Field Theory|
|Thu, 2020-09-24, 9:00 till 12:00||0.002
||Melden Sie sich bitte nur an, wenn Sie die Prüfung verbindlich auch nach Lektüre der Informationen unter https://www.tum.de/die-tum/aktuelles/coronavirus/pruefungen ablegen werden. Keine Prüfungsteilnahme, wenn Sie Quarantäne unterliegen (z.B. Einreisequarantäne), in den 14 Tagen vor der Prüfung Kontakt zu einem COVID-19-Erkrankten hatten oder am Prüfungstag Symptome haben. Personen mit erhöhtem Risiko für einen schweren Verlauf sind gehalten, die notwendigen Maßnahmen zum Eigenschutz zu treffen bzw. von einer Teilnahme abzusehen. // Please only register if you want to take the exam after reading the information at https://www.tum.de/en/about-tum/news/coronavirus/coronavirus-exams/. No participation if you are quarantined (e.g. "Einreisequarantäne") or had contact with a CoViD-19 case in the 14 days before the exam, or have symptoms at the day of the exam.||till 2020-09-13 (cancelation of registration till 2020-09-24)|