Table of Courses
- MINIC: The Challenges of Quantum Gravity
- GIACOMINI: Quantum information tools at the interface between quantum theory and gravity
- DONOGHUE: Perturbative Quantum Gravity
- HAGGARD: The Basics of Loop Quantum Gravity
- NASTASE: String Theory, AdS/CFT and Quantum Gravity
ISQG Official YouTube Playlist: here
Djordje MINIC (Virginia Tech, USA)
The Challenges of Quantum Gravity (1 Lecture: May 16 @ 3 pm CET) (Completed)
This lecture presents an overview of quantum gravity, with a discussion of the challenges it poses for the foundations of physics, general relativity and quantum mechanics. It will explore the state-of-the-art in our current understanding of quantum gravity, and discuss the ongoing investigations and the prospects for the future of quantum gravity.
What is a quantum theory of gravity? I'll discuss various approaches (all theoretical) to this central problem in physics and then I emphasize the need for empirical probes of this fundamental question, and argue for "gravitation of quantum theory'', with specific experimental signatures (triple and higher-order interference) at low energies. As an existing empirical probe, I discuss the observed vacuum energy (Einstein's cosmological constant), perhaps the first measured quantum gravity phenomenon.
arXiv:2212.00901 [hep-th], arXiv:2212.06086 [hep-th], arXiv:2003.00318 [hep-th]
Flaminia GIACOMINI (ETH Zürich, Switzerland)
Quantum information tools at the interface between quantum theory and gravity (4 Lectures: May 22, 23, 24, 25 @ 2 pm CET) (Completed)
John DONOGHUE (University of Massachusetts Amherst, USA)
Perturbative Quantum Gravity (6/7 Lectures: June 8, 13, 15 @ 3 pm CET (Completed Part I), other Lectures in August)
This mini-course will focus on treating General Relativity as a perturbative quantum field theory. We will cover the field-theoretic construction and quantization of the theory. Useful field theory techniques will be introduced. Of course, renormalization will be discussed in detail. There will be an introduction to effective field theory, and we will see how the use of effective field theory techniques allows the calculation of quantum effects at ordinary scales. Finally, we discuss the limits of these techniques and try to point out some of the open directions.
Refs:
- EPFL Lectures on General Relativity as a Quantum Field Theory
- Download your free open-access copy of Dynamics of the Standard Model, which contains material which I will use during this mini-course.
- Everyone should read Feynman’s paper: Quantum Theory of Gravitation. It is informative and also fun.
- Kibble and Utiyama on the construction of GR as a gauge theory
- For the third lecture: Here is an introductory chapter on path integrals from our book A Prelude to Quantum Field Theory. You already have access to the path integral appendix in our book Dynamics of the Standard Model, which is somewhat more advanced. In the appendix section A-6, we discuss Fadeev-Popov ghosts for gauge theories.
- A reference on the background field method is Abbott.
See https://blogs.umass.edu/grqft/ for more details and references.
Preliminaries. Constructing GR as a QFT. Failure of scalar exchange. Energy and momentum as a source. Construction of gauge theories. Need to gauge spacetime translations and why this could work. Equivalence principle. Coordinate changes and the metric. Describing the symmetry. A scalar field. First success -- energy-momentum tensor as a source. Equation of motion. Preview of second success -- Schroedinger equation in a gravitational field and the force law. Preview of the third success -- real QFT -- graviton exchange and the Newtonian potential. Also, some material will be added to some technical details.
Important Path Integral results. Background field method example for QED. Divergences and renormalization. Generalize to get "heat kernel coefficient". Background field expansion for General Relativity. Gauge invariance. Gauge fixing constraint. Ghost stories using Feynman's paper. PI formalism for gauge fixing in QFT. Evaluating the determinant. The ghost Lagrangian for harmonic gauge gravity. Summary of the gravitational path integral.
Review. Free graviton fields. Energy carried by gravitons. Intro to gravity as the square of a gauge theory. Loops of massless matter fields. Curvature squared terms and renormalization. Loops of massive matter fields. Renormalization of the cosmological constant. The cosmological constant does not run. Preview of graviton loops.
Effective Field Theory Day. Basic ideas of EFT. QED as an example. Explicit construction of an EFT from the linear sigma model. Haag's Theorem. Renormalizing a non-renormalizable theory. Heat Kernel methods. Making predictions. Power counting.
EFT treatment of perturbative GR. The derivative/curvature expansion. Matching or measuring. Brief Ostrogradsky comment. Renormalization. The gravitational potential. Pulling out low-energy finite effects. Unitarity techniques. Bending of light. Classical effects from quantum loops. No test particle limit. Non-universality of geodesics. Limitations of the EFT - high energy, low energy issues.
Hal HAGGARD (Bard College, USA)
The Basics of Loop Quantum Gravity (5 Lectures: June 7, 14, 21, 28, July 5 @ 3 pm CET) (Completed)
This course will offer an introduction to Loop Quantum Gravity. We will begin by exploring the challenges of quantum gravity and the motivations behind loop gravity's approach to them. Inspired by the title of this series of courses, we will work to identify a simple, finite degree of freedom, geometrical and gravitational system. This will lead us to the quantum tetrahedron, which we will then use to introduce and illustrate both the Hamiltonian approach of Loop Quantum Gravity and the discrete geometry path integrals known as spin foam models. Building up the theory with the quantum tetrahedron as a constant touchstone, I hope to emphasize the geometry of quantum gravity throughout.
- C. Rovelli, F. Vidotto: Covariant Loop Quantum Gravity, Cambridge Univ. Press, 2014.
C. Rovelli: Quantum Gravity, Cambridge Univ. Press, 2007. - J. Baez, J. P. Muniain: Gauge Fields, Knots, and Gravity, World Scientific, 1994.
- R. Gambini, J. Pullin: Loop Quantum Gravity for Everyone, World Scientific, 2020.
R. Gambini, J. Pullin: A First Course in Loop Quantum Gravity, Oxford University Press, 2011.
A. Ashtekar, J. Pullin (eds.): Loop Quantum Gravity: The First 30 Years, World Scientific, 2017. - T. Thiemann: Modern Canonical Quantum General Relativity, Cambridge Univ. Press, 2007.
M. Bojowald: Quantum Cosmology - A Fundamental Description of the Universe, LNP 835, Springer, 2011. - (See also, C. Bambi, L. Modesto and I. L. Shapiro (eds.): Handbook of Quantum Gravity, Springer, expected in 2023.)
- Why Quantum Gravity?
- Some of the Reasons that Quantum Gravity is Difficult
- Features of the Loop Approach to Quantum Gravity
- Overview of the Course
- Falling cats
- GR as a gauge theory
- Quantum Tetrahedra
Lecture 3 (June 21 @ 3 pm CET)
- Building space
- Spin networks
- Quantum Discreteness
Lecture 4 (June 28 @ 3 pm CET)
- Spin foams
- Discrete Geometry Path Integrals
Lecture 5 (July 5 @ 3 pm CET)
- Frontiers of Loop Quantum Gravity
- Experiments
- Black Holes
- Open Questions
Horatiu NASTASE (São Paulo State University, Brazil)
String Theory, AdS/CFT and Quantum Gravity (4 Lectures: September 21, 28, and October 19, 26 @ 3 pm CET)
In this series of lectures I will explore how the AdS/CFT correspondence helps us understand Quantum Gravity. As AdS/CFT is based on string theory, in the first lecture I will describe the main aspects of supergravity and string theory. In the second lecture, I will describe the main example of the AdS/CFT correspondence, N=4 SYM vs. string theory in the AdS_5xS^5 background, and the variety of nontrivial tests it has passed, including at nontrivial coupling g_s and string length \alpha'. In the third lecture, I will describe the generalizations to gauge/gravity dualities, within string theory ("top-down") and outside ("bottom-up"), and how quantum strings (as opposed to fields for particles) are obtained in the pp wave correspondence, from spin chains. In the fourth lecture, I will describe how purely quantum gravitational effects (at strong coupling) are obtained from field theory in holographic cosmology, a phenomenological application of AdS/CFT to cosmology, leading to an alternative, strongly coupled version, of inflation.
