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Advanced Topics in QFT: from non-perturbative phenomena to gravity

Module NAT3005

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.

Basic Information

NAT3005 is a semester module in language at which is offered irregularly.

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 NAT3005 is Andreas Weiler.

Content, Learning Outcome and Preconditions


  • Solitons in 2D (kink), 3D (vortices), 4D (monopoles)
  • Introduction to homotopy theory and homotopy groups
  • The U(1) problem and the strong CP problem
  • Anomalies and zero modes
  • Instantons and t'Hooft operator
  • QFT in curved space-time
  • Unruh effect
  • Hawking effect
  • Entanglement entropy

Learning Outcome

After successful completion of the module the students are able to understand and model
  1. non-perturbative phenomena in QFT relevant for the theta-vacuum
  2. the violation of anomalous global symmetries by instantons and sphalerons
  3. the quantum theory of inflation
  4. Particle physics in the presence of strong gravitational fields (e.g. near black holes)


QFT1 and QFT2 (highly recommended) and knowledge of general relativity (if possible, especially in Part2).

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Advanced Topics in QFT: from non-perturbative phenomena to gravity Weiler, A. Tue, 10:00–12:00, PH 3343
Thu, 12:00–14:00, PH 3343
and singular or moved dates
UE 2 Exercise to Advanced Topics in QFT: from non-perturbative phenomena to gravity
Responsible/Coordination: Weiler, A.
Thu, 15:15–17:15, PH-Cont. C.3202
Thu, 16:00–18:00, PH-Cont. C.3202

Learning and Teaching Methods

Blackboard lectures and tutorials


Blackboard lectures, possibly but not necessarily with use of slides to show complicated results


  • S. Weinberg - Quantum Field Theory (1 & 2)
  • Rajamaran - Solitons and Instantons
  • L. Parker/D. Toms, Quantum Field Theory in Curved Spacetime, Cambridge Monographs on Mathematical Physics
  • Coleman - Aspects of Symmetry
  • Schwartz - Quantum Field Theory and the Standard Model
  • N.D. Birrell/P.C.W. Davies, Quantum fields in curved space, Cambridge Monographs on Mathematical Physics
  • V.F. Mukhanov/S. Winitzki, Quantum Effects in Gravity, Cambridge University Press

Module Exam

Description of exams and course work

There will be an oral exam of 30 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

  • Explain the relationship between anomalous currents and instantons
  • What are zero modes? What is the t'Hooft operator?
  • What is the theta vacuum?
  • What is a homotopy group and why is it important for gauge theories?
  • What is the Unruh/Hawking effect and how do you calculate it?

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 passing the voluntary test exam during the semester

Exam Repetition

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

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