Advanced Quantum Field Theory
Module PH2185
Module version of SS 2018
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  

SS 2020  SS 2019  SS 2018  SS 2017  SS 2014 
Basic Information
PH2185 is a semester module in English or German language at Master’s level which is offered in summer semester.
This Module is included in the following catalogues within the study programs in physics.
 Specific catalogue of special 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  90 h  10 CP 
Responsible coordinator of the module PH2185 in the version of SS 2018 was Andreas Weiler.
Content, Learning Outcome and Preconditions
Content
 Renormalization group (fixed points etc.)
 Effective action and effective potential
 Spontaneous symmetry breaking, Goldstone bosons
 Nonlinear symmetry realizations, effective Goldstone Lagrangians
 Nontrivial classical field configurations (solitons, instantons etc.) and their quantization
 Anomalies (chiral, gauge, discrete, etc.)
 Basics of supersymmetry (N=1 supersymmetry algebra, WessZumino model etc.)
 Spintwo fields; weak field quantisation of gravitation.
Learning Outcome
The student will be prepared
 to understand the Higgs mechanism;
 to compute quantum corrections to classical potentials;
 to understand topologically nontrivial field configurations both at the classical and the quantum level;
 to understand anomalies and anomaly cancellation;
 to construct a supersymmetric action/theory.
Preconditions
No preconditions in addition to the requirements for the Master’s program in Physics.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
Type  SWS  Title  Lecturer(s)  Dates  Links 

VO  4  Advanced Quantum Field Theory  Weiler, A. 
Wed, 08:00–10:00, PH 3344 Thu, 10:00–12:00, PH 3344 

UE  2  Exercise to Advanced Quantum Field Theory 
Responsible/Coordination: Weiler, A. 
dates in groups 
Learning and Teaching Methods
The modul consists of a lecture and exercise classes.
The lecture is designed for the presentation of the subject, usuallyby 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 in the ecercise classes by the students themselves under the supervision of a tutor in order to develop the skills to solve and explain a physics problem coherently.
Media
Blackboard presentation, additional Powerpoint slides/presentations on demand.
Literature
 Peskin & Schroeder, "An Introduction to Quantum Field Theory"
 Pokorski, "Quantum Field Theory"
 Bailin & Love, "Introduction to Gauge Field Theories"
 Weinberg, "Quantum Theory of Fields" IIII
 Shifman, "Advanced topics in Quantum Field Theory"
 Nakahara, "Geometry, topology and physics"
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 propagator and the interaction vertices for a nonabelian gauge theory in a particular gauge fixing.
 Calculate the 1loop corrections to a nonabelian gauge theory, regularize and renormalize.
 Extract the betafunction coefficients from the above calculation.
 Find the symmetry breaking pattern for a theory with spontaneous symmetry breaking, calculate the Goldstone boson interactions, find potentially anomalous symmetries.
 Derive the selfinteractions of a spin 2 field using the decoupling of the Stueckelberg modes
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
 preparing at least 50 % of the exercises on the exercise sheets and
 presenting at least three exercises at the blackboard and
 participating actively in the tutorials.
Exam Repetition
The exam may be repeated at the end of the semester.