Objectifs :
●​Learn the canonical quantization approach in Loop Quantum Gravity
●​Become familiar with discrete geometry and the theory’s prediction of space’s granular structure
●​Understand quantum polyhedra and the geometric interpretation of LQG states
●​Read and present key introductory research papers in Loop Quantum Gravity

Programme :
1.​ Hamiltonian formulation of GR & Ashtekar variables
2.​ Holonomies, fluxes, and the holonomy-flux algebra
3.​ Kinematical Hilbert space of Loop Quantum Gravity & spin networks
4.​ Geometric operators and their spectra
5.​ Quantum polyhedra and the geometric interpretation of LQG states
6.​ Elements of Covariant Loop Quantum Gravity and spin-foam (path-integral) dynamics
7.​ Applications (e.g. cosmology, black-hole models, semiclassical limits)

Pré-requis :
General Relativity
Advanced Quantum Mechanics (Path Integral)
Group Theory

Equipe pédagogique :
Pietro Dona, Alejandro Perez and Simone Speziale

Méthode pédagogique :
8 sessions × 2h, one per week
Interactive blackboard lectures (1h30) + (30m) Group discussions and Q&A. Occasionally I will show numerical calculation and simulations as a support.

Compétences acquises à l'issue de la formation :
●​ Analyze and evaluate LQG research papers, identifying strengths, limitations, and open questions.
●​ Communicate clearly core ideas of LQG and quantum geometry (spin networks, quantum polyhedra) and discuss the underlying assumptions.
●​ Perform simple calculations in LQG (e.g. computing spectra of geometric operators)

La formation participe à l'objectif suivant :conforter la culture scientifique des doctorants dans leur champ disciplinaire ou en interdisciplinaire