Quantum Field Theory in Curved Space-Time

Module PH2156

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

PH2156 is a semester module in English language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

  • General catalogue of special courses
  • Specific catalogue of special courses for nuclear, particle, and astrophysics

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 PH2156 is Martin Beneke.

Content, Learning Outcome and Preconditions


Classical fields in curved space-time
Field quantization in curved space-time and particle production
Quantum fluctuations in de Sitter space and inflation
Hawking radiation
Back-reaction, effective action and in-in formalism
Metric fluctuations and quantum corrections to inflation
Quantum field theory in extra dimensions [optional]

Learning Outcome

The specifics of field quantization in curved space-time compared to Minkowski space-time;
Basic mathematical formalism;
Applications to the physics of black holes, the early universe, and extra dimensions


Quantization of fields in Minkowski space-time (Quantum Field Theory);
Basic knowledge of classical General Relativity is helpful. With the literature mentioned below, the course may be attended without a course on General Relativity.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VU 5 Quantum Field Theory in Curved Space-Time Beneke, M. einzelne oder verschobene Termine
sowie Termine in Gruppen

Learning and Teaching Methods

Blackboard lecture;
Homework exercises preceded by a tutorium.


Blackboard, website.


[1] N.D. Birrell/P.C.W. Davies, "Quantum fields in curved space", Cambridge Monographs on Mathematical Physics
[2] V.F. Mukhanov/S. Winitzki, "Quantum Effects in Gravity", Cambridge University Press
[3] L. Parker/D. Toms, "Quantum Field Theory in Curved Spacetime", Cambridge Monographs on Mathematical Physics
[4] To review the basics of General Relativity: Chapter 2 of S. Weinberg "Gravitation and Cosmology"

[5] Journal Papers

Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 90 minutes.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

Condensed Matter

When atoms interact things can get interesting. Fundamental research on the underlying properties of materials and nanostructures and exploration of the potential they provide for applications.

Nuclei, Particles, Astrophysics

A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.