The Courses

Slides:

1. First lecture

2. Second lecture

3. Third lecture

+. Mathematica notebook to compute Asymptotic Symmetries and Charges in 3d Gravity

References:

Mentioned in lecture 1

• A short review on Noether's theorems, gauge symmetries and boundary terms - Máximo Bañados, Ignacio A. Reyes

• Quantization of Gauge Systems - Marc Henneaux and Claudio Teitelboim

• Black Hole Entropy is Noether Charge - Robert Wald

• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy - Vivek Iyer, Robert M. Wald

• Covariant phase space with boundaries - Daniel Harlow, Jie-qiang Wu

• Advanced Lectures on General Relativity - Geoffrey Compère, Adrien Fiorucci

Mentioned in lecture 2

• Quantum Gravity in 2+1 Dimensions - S. Carlip

• BMS Particles in Three Dimensions - Blagoje Oblak

• Asymptotic dynamics of three-dimensional gravity - Laura Donnay

Slides:

1. First lecture

2. Second lecture

3. Third lecture

References:

Reviews

• Quantum Gravity in 2+1 Dimensions - S. Carlip

• Introduction to Loop Quantum Gravity and Spin Foams - Alejandro Perez

• An elementary introduction to loop quantum gravity - Norbert Bodendorfer

• Introductory lectures to loop quantum gravity - Pietro Dona, Simone Speziale

Books

• Modern Canonical Quantum General Relativity - Thomas Thiemann (for math oriented students)

• Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory - Carlo Rovelli, Francesca Vidotto (more physical ideas)

• A First Course in Loop Quantum Gravity - Rodolfo Gambini, Jorge Pullin (indicated for undergrad)

Useful papers

• A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity - Alberto S. Cattaneo, Alejandro Perez

Slides:

1. First lecture

2. Second lecture

3. Third lecture

Slides: All the lectures

References:

Books:

• Quantum Fields in Curved Space - N. D. Birrell, P. C. W. Davies

• Quantum Field Theory in Curved Spacetime - Leonard Parker and David Toms

• Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics - Robert Wald

• Modeling Black Hole Evaporation - Alessandro Fabbri and José Navarro-Salas

• Aspects of Quantum Field Theory in Curved Spacetime - Stephen A. Fulling

Part 1:

• Bosonic and fermionic Gaussian states from Kähler structures - Lucas Hackl, Eugenio Bianchi

• Quantum Fields in Curved Space-Times - A. Ashtekar and A. Magnon

• Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics - Robert Wald

Slides: All the lectures

References:

• Quantum gravity, shadow states, and quantum mechanics - Abhay Ashtekar, Stephen Fairhurst, Joshua L. Willis

• Quantum Nature of the Big Bang: Improved dynamics - Abhay Ashtekar, Tomasz Pawlowski, Parampreet Singh

• Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology - Mercedes Martin-Benito, Guillermo A. Mena Marugan, Javier Olmedo

• Alleviating the Tension in the Cosmic Microwave Background using Planck-Scale Physics - Abhay Ashtekar, Brajesh Gupt, Donghui Jeong, V. Sreenath

I will give an introduction to group field theory, explaining its relation to spinfoam models and canonical loop quantum gravity. In the second part of the class, I will focus on condensate states, which capture the homogeneity and isotropy of cosmological space-times, and show that the emergent dynamics for the total volume of these condensate states give a modified Friedman equation very similar to what is found in loop quantum cosmology.

Slides:

1. First lecture

2. Second lecture

References:

• Group field theory as the 2nd quantization of Loop Quantum Gravity - Daniele Oriti

• A Model of three-dimensional lattice gravity - Boulatov

• Spacetime as a Feynman diagram: the connection formulation - Reisenberger, Rovelli

• Group field theory: An Overview - Freidel

• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates - Daniele Oriti, Lorenzo Sindoni, Edward Wilson-Ewing

• Cosmology from Group Field Theory Formalism for Quantum Gravity

Slides: slides of the lecture

The advanced LIGO and Virgo detectors have now observed gravitational waves from nearly fifty binary-black-hole mergers and several neutron-star binaries during their first two and a half observing runs. These detections allowed our Universe to be observed in gravitational waves for the first time, and they have confirmed many of the predictions of general relativity. I will discuss some of these results and their implications for testing the predictions of classical and quantum gravity. I will also review the plans for the next generation of gravitational-wave detectors and summarize their capabilities. In particular, I will highlight how gravitational-wave detectors will be able to observe gravitational-wave memory effects, which can give insights into the infrared structure of the gravitational interaction.

Slides: slides of the lecture

References:

• LIGO/Virgo papers: GWTC-2, arXiv:2010.14527; GWTC-1, arXiv:1811.12907; Tests of GR with GWTC-2, arXiv:2010.14529; Tests of GR with GWTC-1, arXiv:1903.04467

• Reviews on testing GR with gravitational waves: Ch. III of arXiv:1806.05195; 2-paper review series, arXiv:1801.03208 and arXiv:1801.03587

• Detecting GW memory: arXiv:1605.01415, arXiv:1911.12496, arXiv:2002.01821, arXiv:2105.02879

Slides: slides

Lecture 1: Slides

• Entanglement entropy

• Page curve

• Entropy production

• Thermodynamics from entanglement

References:

• Quantum Processes, Systems, and Information - Schumacher and Westmoreland

• Average Entropy of a Subsystem - Page

• Typical entanglement entropy in the presence of a center - Bianchi and Donà

Lecture 2: Slides

• Entanglement in Gaussian states

• Kähler structures and time evolution

• Quantum fields and subalgebras

• The area law

References:

• Colloquium: Area laws for the entanglement entropy - Eisert Cramer and Plenio

• Entropy and Area - Srednicki

• Entropy of a subalgebra of observables and the geometric entanglement entropy - Bianchi and Satz

• Bosonic and fermionic Gaussian states from Kähler structures - Bianchi and Hackl

Mathematica Notebooks:

1. Entanglement Entropy of Two Spins

2. Entanglement Entropy of a Random Pure State

3. Entanglement Entropy Evolution with Random Matrix Hamiltonian

4. Mutual Information and Correlations in Random States

I will introduce the notion of quantum reference frame (QRF) as a reference frame associated to a physical (quantum) system. I will mainly focus on two different approaches. In the first approach that I will review, which provides a more quantum information perspective, QRFs have been used to overcome superselection rules. In the second approach, which has a more foundational flavour, I will show how to change perspective between two different QRFs, and how this allows us to generalise the notion of covariance of physical laws and extend the Galilean symmetry transformations. I will also show an equivalent derivation of this second approach which makes use of a symmetry principle.

I will then compare how the differences between the two approaches can be understood in terms of group-averaging operations. Finally, I will argue that studying QRFs can shed light into some questions at the interface of quantum theory and gravity, such as the formulation of the Einstein Equivalence Principle for a superposition of spacetimes.

Slides: slides

References:

• Reference frames, superselection rules, and quantum information - Stephen D. Bartlett, Terry Rudolph, Robert W. Spekkens

• Quantum mechanics and the covariance of physical laws in quantum reference frames - Flaminia Giacomini, Esteban Castro-Ruiz, Caslav Brukner

• A change of perspective: switching quantum reference frames via a perspective-neutral framework - Augustin Vanrietvelde, Philipp A Hoehn, Flaminia Giacomini, Esteban Castro-Ruiz

• Quantum reference frame transformations as symmetries and the paradox of the third particle - Marius Krumm, Philipp A. Hoehn, Markus P. Mueller

• Einstein's Equivalence principle for superpositions of gravitational fields - Flaminia Giacomini, Caslav Brukner

What happens to a black hole at the end of its evaporation? This a concrete physical problem, with possible astrophysical implications, where Loop Quantum Gravity can be applied. In the lecture, I illustrate the role of quantum gravity in the physics of black holes, and discuss the possibility of quantum tunneling form black holes to white holes.

Slides: slides

References:

• The End of a Black Hole’s Evaporation - Fabio D'Ambrosio, Marios Christodoulou, Pierre Martin-Dussaud, Carlo Rovelli, Farshid Soltani

• Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunnelling - Hal Haggard, Carlo Rovelli

• White Holes as Remnants: A Surprising Scenario for the End of a Black Hole - Eugenio Bianchi, Marios Christodoulou, Fabio D'Ambrosio, Hal M. Haggard, Carlo Rovelli

A number of approaches to four-dimensional quantum gravity, such as loop quantum gravity and holography, situate areas as their fundamental variables. However, this choice of kinematics can easily lead to gravitational dynamics peaked on flat spacetimes. We show that this is due to how regions are glued in the gravitational path integral via a discrete spin foam model. We introduce a family of "effective" spin foam models that incorporate a quantum area spectrum, impose gluing constraints weakly, but as strongly as allowed by uncertainty relations, and leverage the discrete general relativity action to specify amplitudes. These effective spin foam models avoid flatness, have a rich semiclassical regime, and have been used to find new results on dynamics and geometrical expectation values in both Euclidean and Lorentzian four-dimensional quantum gravity.

Slides: part 1 and part 2

References:

• Effective Spin Foam Models for Lorentzian Quantum Gravity - Seth K. Asante, Bianca Dittrich, José Padua-Arguelles

• Discrete gravity dynamics from effective spin foams - Seth K. Asante, Bianca Dittrich, Hal M. Haggard

• Effective Spin Foam Models for Four-Dimensional Quantum Gravity - Seth K. Asante, Bianca Dittrich, Hal M. Haggard

• The Degrees of Freedom of Area Regge Calculus: Dynamics, Non-metricity, and Broken Diffeomorphisms - Seth K. Asante, Bianca Dittrich, Hal M. Haggard

• Modified Graviton Dynamics From Spin Foams: The Area Regge Action - Bianca Dittrich

• Lorentzian angles and trigonometry including lightlike vectors - Rafael Sorkin

In this lecture, I will try to convince you that writing a spin foam transition amplitude is not that complicated. We will review the state of the art techniques to compute transition amplitude for the EPRL model.

Slides: slides

References:

• Jupiter notebooks with calculations in the Ponzano-Regge model. One vertex, three vertices, one bubble.

• The original Ponzano-Regge paper

• The sl2cfoam and sl2cfoam-next git repositories

• many other clickable references in the slides

In this lecture, I will introduce to you the exciting proposals for experiments that will test the quantum nature of gravity. These experiments do not involve huge particle accelerators nor astrophysical observations. Instead, they rely on having quantum control of a relatively large piece of matter and base their claims on results in quantum information theory. We will review the principles behind these experiments, the technical challenges involved, and the implications of their results on theories of gravity.

Slides: slides

References:

• Can Gravitons Be Detected? - Tony Rothman, Stephen Boughn

• A Spin Entanglement Witness for Quantum Gravity - Sougato Bose, Anupam Mazumdar, Gavin W. Morley, Hendrik Ulbricht, Marko Toroš, Mauro Paternostro, Andrew Geraci, Peter Barker, M. S. Kim, Gerard Milburn

• Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity - Chiara Marletto, Vlatko Vedral

• Observable quantum entanglement due to gravity - Tanjung Krisnanda, Guo Yao Tham, Mauro Paternostro, Tomasz Paterek

• Non-Gaussianity as a signature of a quantum theory of gravity - Richard Howl, Vlatko Vedral, Devang Naik, Marios Christodoulou, Carlo Rovelli, Aditya Iyer

• A no-go theorem on the nature of the gravitational field beyond quantum theory - Thomas D. Galley, Flaminia Giacomini, John H. Selby

• Picturing Quantum Processes - Bob Coecke, Aleks Kissinger

• Witnessing non-classicality beyond quantum theory - Chiara Marletto, Vlatko Vedral