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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 2018/9

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 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 workloadContact hoursCredits (ECTS)
300 h 105 h 10 CP

Responsible coordinator of the module PH2041 in the version of WS 2018/9 was Andreas Weiler.

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

Learning Outcome

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 module like “Relativity, particles, fields” (PH2040).

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 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 modul consists of a lecture and exercise groups and a central exercise.

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 exercisis instructor in order to develop the skills to solve and explain a physics problem coherently. In the central exercise the learning contents are deepened and practiced, as well as further questions to the lecture are answered.


Blackboard, possibly supplemented with slides. Homework problems for deepening and practising the learned topics


  • M. Peskin & D.V. Schroeder, "An Introduction to Quantum Field Theory" (Taylor & Francis)
  • S. Weinberg, "Quantum Theory of Fields" (Cambridge University Press)
  • M.D. Schwartz, "Quantum Field Theory and the Standard Model" (Cambridge University Press)

Module Exam

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.

In the exam the following learning aids are permitted: Students can bring up to 4 pages (i.e. 2 two-sided A4 sheets) of handwritten notes, but no books or other notes. You will receive scratch paper from us

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,

Exam Repetition

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

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