Introduction to quantum field theory on curved background

fall 2025: 3/0 Ex

Annotation:

Hamiltonian formalism in field theory, 3+1 splitting, classical Green functions. Quantization on a curved background, Fock basis, coherent states, vacuum state, normal ordering, Bogoliubov transformation, S-matrix, amplitudes and generating functional. Static spacetimes, diagonalization of the Hamiltonian, thermal states, quantum Green functions, their analytical properties and singular structure, Wick rotation. Moving mirrors, cosmological particle creation, Unruh effect, particle detectors. Hawking effect, choice of modes and vacuum state. Quantization in de Sitter spoacetime.

The course is intended for students in the Master's and PhD programs.

Knowledge of General Relativity and Quantum Mechanics on the level of introductory courses is assumed. Previous experience with Quantum Field Theory gives a big advantage, but it is not a necessary requirement.

Lectures in fall 2025:

Lectures are scheduled each Thursday at 10:40–12:05 in the ITP lecture room at the 10th floor in Troja.

Lectures are taught in person.

Recordings from previous years are available on a special page, the address of which was sent to enrolled students.

If anyone is interested in watching recordings of the lectures without enrolment, please, contact the lecturer by email.

Lectures are given in Czech this term. However, recordings of the lectures in English are available from 2021. Students interested in taking the course in English should contact the lecturer. Individual guidance through the course in English is possible.

Exam:

Zkouška se koná v následujících termínech:

čtvrtek 4.6. 11:00 ÚTF
středa 10.6. 11:00 ÚTF
středa 17.6. 11:00 ÚTF
středa 24.6. 11:00 ÚTF
středa 1.7. 11:00 ÚTF
středa 8.7. 11:00 ÚTF
úterý 21.7. 11:00 ÚTF
středa 9.9. 11:00 ÚTF

Další termíny po domluvě s prof. Bičákem nebo prof. Krtoušem.

Zkouška se skládá z písemné (na základě odevzdaných domácích úkolů) a ústní části (2 otázky z vyložené látky).

Literature:

Wald R. M.: Quantum Field Theory in Curved Spacetime and Black Hole (University Of Chicago Press, Chicago, 1994)
Birrell N. D., Davies P. C. W.: Quantum fields in curved space (Cambridge University Press, Cambridge, 1984)
Mukhanov V., Winitzki S.: Introduction to Quantum Effects in Gravity (Cambridge University Press, Cambridge, 2007)
Parker L., Toms D.: Quantum Field Theory in Curved Spacetime (Cambridge University Press, Cambridge, 2009)
Fulling S. A.: Aspects of Quantum Field Theory in Curved Spacetime Thermodynamics (Cambridge University Press, Cambridge, 1989)
Frolov V., Novikov I.: Black Hole Physics - Basic Concepts and New Developments (Kluwer Academic Publisher, Dordrecht, 1998)
Fabbri A., Navarro-Salas J.: Modeling Black Hole Evaporation (Imperial College Press, London, 2005)
Hollands S., Wald R. M.: Quantum fields in curved spacetime, Phys. Rept. 574, 1 (2015)
Jacobson T.: Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect, arXiv: gr-qc/0208048 (2002)
Dewitt B. S.: Quantum Field Theory In Curved Space-Time, Phys. Rept. 19, 295 (1975)