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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.

Module version of SS 2019 (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 2019SS 2012

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.

  • 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 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 (warped) extra dimensions

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

VO 4 Quantum Field Theory in Curved Space-Time Beneke, M. Thu, 12:00–14:00, PH 3344
Tue, 08:00–10:00, PH 3344
UE 2 Exercise to Quantum Field Theory in Curved Space-Time singular or moved dates
and dates in groups

Learning and Teaching Methods

Blackboard lecture;
Homework exercises preceded by a tutorium.

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 tutor in order to develop the skills to solve and explain a physics problem coherently.


Blackboard, website.

Course 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

There will be a written exam of 120 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: Question on topics such as Hawking radiation and others from the table of contents

Exam Repetition

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

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