- Term: Winter 2024.
- Course codes: AMATH872 / PHYS785
- Instructor: Achim Kempf
- Prerequisite: AMATH673 or PHYS702 or consent of instructor. Some knowledge of general relativity.
- Time/venue: Tuesdays and Thursdays 4-5:20pm in the Alice room at Perimeter Institute. First lecture: Tue, Jan 9.
- Reading week: no lectures from Sat, Feb 17, 2024 to Sun Feb 25, 2024
- Discussions/tutorial with prof: TBA
- Office hours: by arrangement.
This course introduces quantum field theory from scratch and then develops the theory of the quantum fluctuations of fields and particles. We will focus, in particular, on how quantum fields are affected by curvature and by spacetime horizons. This will lead us to the Unruh effect, Hawking radiation and to inflationary cosmology. Inflationary cosmology, which we will study in detail, is part of the current standard model of cosmology which holds that all structure in the universe - such as the distribution of galaxies - originated in tiny quantum fluctuations of a scalar field and of space-time itself. For intuition, consider that quantum field fluctuations of significant amplitude normally occur only at very small length scales. Close to the big bang, during a brief initial period of nearly exponentially fast expansion (inflation), such small-wavelength but large-amplitude quantum fluctuations were stretched out to cosmological wavelengths. In this way, quantum fluctuations are thought to have seeded the observed inhomogeneities in the cosmic microwave background - which in turn seeded the condensation of hydrogen into galaxies and stars, all closely matching the increasingly accurate astronomical observations over recent years. The prerequisites for this course are a solid understanding of quantum theory and some basic knowledge of general relativity, such as FRW spacetimes.
- The grades are currently planned to be based on a project, and essay and a presentation. Details TBA.
Health precautions (permanent)
- If you have cold/flu/covid symptoms, do not come to class. Do the right thing, which is taking care of yourself and getting healthy first.
- For Lecture Videos (of my previous teaching), scroll down to the bottom of this page.
- All important updates will always be posted here.
Lectures, lecture notes and videos:
In the list below, the videos are from my pre-pandemic teaching of this course. New recordings are planned for Winter 2024.
Feb 27 (Tue), Lecture 13: Notes, Video
Conservation and covariance of the CCRs. Stone von Neumann theorem. General Bogolubov maps.
Feb 29 (Thu), Lecture 14: Notes, Video
K.G. field in FRW Spacetimes. Conformal time. Chi field. Hamiltonians. Energy momentum tensor.
Remark to those who are not enrolled: I invite anybody to download these lecture notes for study purposes and to view the recordings, even without being enrolled in the course. If you do, please send me an email though, I'd just like to know. Thanks!
To some extent, we will follow this textbook: V. Mukhanov, Sergei Winitzki, Introduction to Quantum Effects in Gravity, Cambridge University Press, June 2007. It has plenty of homework problems including solutions. I strongly recommend making use of them.
- N.D. Birrell, P.C.W. Davies, Quantum Fields in Curved Space, CUP, 1984.
- S.A. Fulling, Aspects of Quantum Field Theory in Curve Space-Time, CUP, 1989.
- A.R. Liddle, D. H. Lyth, Cosmological Inflation and Large-Scale Structure, CUP, 2000.
- T. Jacobson, Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect, http://arxiv.org/abs/gr-qc/0308048
- L.H. Ford, Quantum Field Theory in Curved Spacetime, http://arxiv.org/abs/gr-qc/9707062