Introduction to quantum field theory on curved background

lecture materials

fall 2021: 3/0 Ex

Annotation:

3+1 splitting 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 2021:

Lectures were scheduled each Thursday at 9:50–12:15 in lecture room T1.

Lectures were taught in person.

Lectures were recorded. Recordings are available here.

Lectures were given in English.

Exam:

Times scheduled for the exams are listed in SIS.

The exam has an oral form. The student gets two theoretical questions - one about general formalism, and other about applications. She/he has sufficient time to prepare the answers.

The preferred form of the exam is in person. But in necessary cases, it is possible to take the exam online. Please, contact the lecturer a day before the exam in such a case.

It will be possible to schedule the exam after the winter term. Please contact the lecturer.

Lectures by date:

Recordings are split by the day on which they were given.

Recordings can be watched in the following player or downloaded as mp4 below.

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September 30, 2021: Introduction [mp4 14m 44MB]; Functional notation [mp4 42m 135MB]; Covariant phase space 1 [mp4 93m 359MB]
October 7, 2021: Covariant phase space 2 [mp4 22m 81MB]; 3+1 splitting [mp4 61m 244MB]; Quantization (Harmonic oscilator) 1 [mp4 55m 196MB]
October 14, 2021: Quantization (Harmonic oscilator) 2 [mp4 28m 196MB]; Particle interpretation 1 [mp4 110m 432MB]
October 21, 2021: Particle interpretation 2 [mp4 17m 53MB]; Coherent states [mp4 63m 240MB]; Green functions [mp4 129MB]; Static spacetimes 1 [mp4 26m 97MB]
October 28, 2021: Static spacetimes 2 [mp4 60m 238MB]; Properties of Green functions 1 [mp4 70m 278MB]
November 04, 2021: Holomorphic representation [mp4 105m 425MB]
November 11, 2021: In-out formalism 1 [mp4 72m 280MB]; In-out formalism 2 [mp4 62m 220MB]
November 25, 2021: In-out formalism - generating functionals [mp4 134m 473MB]
December 2, 2021: Applications [mp4 108m 339MB]; Unruh effect - coordinates [mp4 12m 28MB]
December 9, 2021: Unruh effect [mp4 110m 388MB]
December 16, 2021: Hawking effect 1 [mp4 146m 570MB]
Unfortunately, the original lecture has been recorded out of focus. This is a new version containing the technical part of the original lecture.; Hawking effect 2 - evaporation [mp4 17m 80MB]
Additional qualitative notes on the black-hole evaporation. They have not been presented at the original lecture.; Hawking effect 3 - HH vacuum [mp4 30m 127MB]
Comments about Hartle-Hawking vacuum. It is slightly more detailed version than in the original lecture.
January 6, 2022: Quantization in de Sitter space [mp4 117m 413MB]

Lectures by topic:

Recordings are split by topic. If the topic was discussed in consecutive lectures, some introductory comments in later lectures are omitted.

Recordings can be watched in the following player or downloaded as mp4 below.

Player:

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Notes:

Notes are in Czech, but mostly equations.

Handouts:

Some auxiliary material.

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)