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Introduction to Loop Quantum Gravity
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Introduction to Loop Quantum Gravity
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Academic year 2024/2025
- Teacher
- Lorenzo Fatibene (Lecturer)
- Teaching period
- Jan-Mar
- Type
- Elective
- Credits/Recognition
- 6
- Course disciplinary sector (SSD)
- MAT/07 - mathematical physics
- Delivery
- Formal authority
- Language
- English
- Attendance
- Optional
- Type of examination
- Oral
- Prerequisites
- Not much, general knowledge of analysis, geometry and mathematical physics. I can give material to fill in prerequisites on demand.
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Sommario del corso
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Program
We consider mathematical structures used in loop quantum gravity (LQG) starting from classical GR to the introduction of spin network Hilbert space and operators on it to represent geometric quantities. From a physical viewpoint, LQG is a proposal for a generally covariant QFT. From the mathematical viewpoint one sees in action classical field theories, bundle theory, holonomies of connections on manifolds, analysis on (bare) manifolds, group representation theory (for SU(2)), Clifford algebras, topological obstructions, and, finally, operators on Hilbert spaces. All in action to solve the specific problem of describing quantum gravity.
Suggested readings and bibliography
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Notes
Hours: 30 Period: Jan - Feb 2025
Classes:
Jan 9 15-18 - Room 5 - Palazzo Campana [3]
Connessioni principali, trasporto parallelo, olonomia.
Teorema di rappressentazione
Jan 10 9:30-12:30 - Room 5 - Palazzo Campana [6]
Connessioni discrete, fibrati principali su reticoli, misura di Haar, funzionali cilindrici su un reticolo.
Jan 13 9-12 - Room 5 - Palazzo Campana [9]
Raffinamenti di reticoli e struttura diretta dei funzionali cilindrici
Spazio di Hilbert degli stati cinematici, su un reticolo e il loro limite diretto.
Teorema di Peter-Weyl e basi ortonormali degli stati cinematici.
Stati gauge-invarianti e spin networks.
Jan 15 14-17 - Room 5 - Palazzo Campana [12]
Teoria delle rappresentazioni di SU(2)=Spin(3,0)Jan 20 9-13 [15]
Intertwiners e rappresentazione grafica.
Spin networks. Operatori di olonomia e di Lie sulle spin networks.Jan 23 9-13 [18]
...
Materiale e registrazioni qui.
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