Aix Marseille Univ., Univ. de Toulon, CNRS, CPT, Marseille, France
fall 2022: 2/0 Ex
Abstract:
A brief introduction to loop quantum gravity’s spin networks and quanta of space
Indicative program for an introductory course to loop quantum gravity.
Individual lectures: 90 minutes.
Recommended background: classical general relativity, Hamiltonian structure of gauge theories, basics of group representation theory, quantum field theory.
Information about lectures:
The course contains ten lectures given by Prof. Speziale. The lectures took place in the period October 31st – November 11th. The lectures were given in English.
Enrolled students will prepare a short review of a given topic to obtain credits for the course. They will present these reviews during 1-2 additional seminars, which will take place at the beginning of the summer semester.
Students should enroll for the lecture in the summer semester.
Introduction: why QG? Why is it hard? Basics of perturbative quantum gravity and motivations for a background-independent approach.
Tue Nov 1, 18:10Lecture 2
Canonical gravity: brief review of ADM formalism including surface terms, the problem of time and Dirac observables, difficulties with the Wheeler-De Witt approach
Wed Nov 2, 17:20Lecture 3
General relativity as an SU(2) gauge theory: derivation of the Ashtekar-Barbero variables
Thu Nov 3, 16:30Lecture 4
Gauge-invariance, Wilson loops and tools from lattice gauge theory
Fri Nov 4, 14:00Lecture 5
SU(2) invariants and Penrose’s spin networks states
Mon Nov 7, 18:10Lecture 6
Holonomy-Flux algebra, area and volume operators; quanta of space
Tue Nov 8, 18:10Lecture 7
Semiclassics on a fixed graph: coherent states, spin networks as a collection of fuzzy polyhedra
Wed Nov 9, 16:30Lecture 8
Approaches to the dynamics: brief overview of canonical and covariant models
Thu Nov 10, 16:30Lecture 9
More on covariant spin foam models: Regge calculus, SL(2, C) unitary irreps and the EPRL model
Fri Nov 11, 14:00Lecture 10
Conclusions: what have we achieved so far, and what are we trying to achieve next
Lecture recordings:
Lectures can be played directly in the following player or they can be downloaded as mp4 files from the list below.
Materials for download:
To download mp4 file you may need to click by the right mouse button and choose the download from the menu.
Literature:
C. Rovelli, F. Vidotto: Covariant Loop Quantum Gravity, Cambridge Univ. Press, 2014.
C. Rovelli: Quantum Gravity, Cambridge Univ. Press, 2007.
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.
