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Quantum Field Theory

Module PH2041

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2016/7

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 2019/20WS 2018/9WS 2017/8WS 2016/7WS 2015/6WS 2013/4WS 2010/1

Basic Information

PH2041 is a semester module in English or German language at Master’s level which is offered in winter semester.

This module description is valid from WS 2013/4 to SS 2017.

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
300 h 110 h 10 CP

Responsible coordinator of the module PH2041 in the version of WS 2016/7 was Martin Beneke.

Content, Learning Outcome and Preconditions


  • Functional (path integral) quantisation of bosonic and fermionic fields
  • Green functions
  • Perturbation expansion, Feynman diagrams
  • Particle states, LSZ reduction and cross sections
  • Gauge invariance and quantisation of non-abelian gauge theories
  • Ward-Takahashi identities
  • Loop calculations and UV regularisation
  • Dimensional regularisation
  • Renormalisation, in particular of gauge theories
  • Next-to-leading order effects in gauge theories (e.g. anomalous
  • magnetic moment, infrared divergences and soft bremsstrahlung)
  • Effective field theory
  • Renormalisation group, running couplings and masses

Learning Outcome

After successful completion of the module the student will be prepared

  • 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 info

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 5 Quantum Field Theory Beneke, M. Dybalski, W. Wed, 12:00–14:00, PH HS3
Wed, 14:00–16:00, PH HS3
Mon, 12:00–14:00, PH HS3
UE 1 Exercise to Quantum Field Theory Vaudrevange, P.
Responsible/Coordination: Beneke, M.
dates in groups
UE 1 Large Exercise to Quantum Field Theory Vaudrevange, P.
Responsible/Coordination: Beneke, M.
Wed, 14:00–16:00, PH HS3

Learning and Teaching Methods

The course is accompanied by homework problems.


Blackboard, possibly supplemented with slides.


  • Peskin & Schroeder, "An Introduction to Quantum Field Theory"
  • Itykson & Zuber, "Quantum Field Theory"
  • Bailin & Love, "Introduction to Gauge Field Theories"

Module Exam

Description of exams and course work

The learning outcome is tested in a written exam of 180 minutes duration. Participation in tutorials is strongly recommended.

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 following conditions

  1. The student prepared at least 50% of the exercises on the exercise sheets and
  2. presented at least three exercises at the blackboard and
  3. actively participated in the tutorials.

Exam Repetition

The exam may be repeated at the end of the semester.

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