Introduction to the Loop Quantum Gravity


Simone Speziale

Aix Marseille Univ., Univ. de Toulon, CNRS, CPT, Marseille, France

fall 2022: 2/0 Ex


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.

The initial meeting for scheduling the seminars (and announcing the available topics) will take place on Tuesday 14.2. at 13:10 in the seminar room A1032UTF of the Institute of Theoretical Physics. For additional info contact

The course is supported by Institute of Particle and Nuclear Physics and Institute of Theoretical Physics of FMP, Charles University.

Syllabus and lecture schedule:

Mon Oct 31, 18:10 Lecture 1
Introduction: why QG? Why is it hard? Basics of perturbative quantum gravity and motivations for a background-independent approach.
Tue Nov 1, 18:10 Lecture 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, 17:20 Lecture 3
General relativity as an SU(2) gauge theory: derivation of the Ashtekar-Barbero variables
Thu Nov 3, 16:30 Lecture 4
Gauge-invariance, Wilson loops and tools from lattice gauge theory
Fri Nov 4, 14:00 Lecture 5
SU(2) invariants and Penrose’s spin networks states
Mon Nov 7, 18:10 Lecture 6
Holonomy-Flux algebra, area and volume operators; quanta of space
Tue Nov 8, 18:10 Lecture 7
Semiclassics on a fixed graph: coherent states, spin networks as a collection of fuzzy polyhedra
Wed Nov 9, 16:30 Lecture 8
Approaches to the dynamics: brief overview of canonical and covariant models
Thu Nov 10, 16:30 Lecture 9
More on covariant spin foam models: Regge calculus, SL(2, C) unitary irreps and the EPRL model
Fri Nov 11, 14:00 Lecture 10
Conclusions: what have we achieved so far, and we 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:

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