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Advanced Quantum Field Theory

Module PH2185

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 SS 2022 (current)

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 2022SS 2021SS 2020SS 2019SS 2018SS 2017SS 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 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 90 h 10 CP

Responsible coordinator of the module PH2185 is Martin Beneke.

Content, Learning Outcome and Preconditions


  • Quantization and Renormalization of non-abelian gauge theories
  • Spin-2 fields and weak-field quantization of gravity
  • Effective action and effective potential
  • Spontaneous symmetry breaking, Goldstone bosons
  • Non-linear symmetry realizations, effective Goldstone Lagrangians
  • Electroweak symmetry breaking and the Higgs boson
  • Infrared divergences and factorization
  • Anomalies
  • [Optional] Basics of supersymmetry (N=1 supersymmetry algebra, Wess-Zumino model etc.)
  • [Optional] Non-trivial classical field configurations (solitons, instantons etc.) and their quantization

Learning Outcome

The student will be prepared

  • to understand the Higgs mechanism;
  • to understand the QFT of spin-1 and spin-2 fields;
  • to understand the concept of non-linear symmetry realization and Goldstone bosons;
  • to understand anomalies and anomaly cancellation;
  • to understand infrared divergences and their physical significance


No formal preconditions in addition to the requirements for the Master’s program in Physics. However,

knowledge of basic quantum field theory including renormalization will be assumed.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Advanced Quantum Field Theory Beneke, M. Wed, 08:00–10:00, PH 3344
Thu, 10:00–12:00, PH 3344
and singular or moved dates
UE 2 Exercise to Advanced Quantum Field Theory Ji, Y.
Responsible/Coordination: Beneke, M.
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 supervizor in order to develop the skills to solve and explain a physics problem coherently.


Blackboard presentation, additional Powerpoint slides/presentations on demand.

Please consult the webpage for up-to-date

information on the course, including its schedule (page activated a few weeks before the start of the course)


  • M.E. Peskin & D.V. Schroeder: An Introduction to Quantum Field Theory, Westview Press, (1995)
  • S. Pokorski: Gauge Field Theories, Cambridge University Press, (2000)
  • D. Bailin & A. Love: Introduction to Gauge Field Theory, CRC Press, (2018)
  • S. Weinberg: The Quantum Theory of Fields, I-III, Cambridge University Press, (2005)
  • M. Shifman: Advanced Topics in Quantum Field Theory, Cambridge University Press, (2012)
  • M. Nakahara: Geometry, Topology and Physics, CRC Press, (2003)

Module Exam

Description of exams and course work

There will be an oral exam of 25 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 non-abelian gauge theory in a particular gauge fixing.
  • Calculate the 1-loop corrections to a non-abelian gauge theory, regularize and renormalize.
  • Extract the beta-function 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 self-interactions 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 mid-term of

  • preparing at least 50 % of the exercises on the exercise sheets and
  • 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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