Quantum Field Theory
Module PH2041
Module version of WS 2019/20
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 2020/1  WS 2019/20  WS 2018/9  WS 2017/8  WS 2016/7  WS 2015/6  WS 2013/4  WS 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 EliteMaster Program Theoretical and Mathematical Physics (TMP)
If not stated otherwise for export to a nonphysics 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 2019/20 was Andreas Weiler.
Content, Learning Outcome and Preconditions
Content
 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 highenergy reactions;
 to quantise nonAbelian 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.
Preconditions
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
Type  SWS  Title  Lecturer(s)  Dates  Links 

VO  5  Quantum Field Theory  Beneke, M. Dybalski, W. 
Wed, 14:00–16:00, PH HS3 Wed, 12:00–14:00, 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 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.
Media
Blackboard, possibly supplemented with slides. Homework problems for deepening and practising the learned topics
Literature
 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 crosssection of a 2>2 process.
 Calculate a 1loop diagram, regularize and renormalize
 Integrate out a heavy particle and determine the resulting effective field theory
 Determine the Noethercurrent 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 twosided 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 midterm 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.