March 23 - April 3, 2007
Zakopane, Poland
The First
Quantum Geometry and Quantum Gravity School
Programme of lectures
Lectures will start everyday at 14.00. Every lecture will take 45 minutes, and there will be 15 minutes of break between lectures.
Note that first lecture starts Mar, 23 at 14.00, while the last lecture ends Apr, 3 at 19.00.
Contents and abstracts of lectures
Laurent Freidel: Spin-Foam Models |
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1. General introduction to spin foams 2. 3D Gravity and introduction to some group theory 3. The Ponzano-Regge model derivation and its properties 4. The Ponzano-Regge model + matter 5. Effective field theory |
Pawe³ Kasprzak: Locally compact quantum Lorentz groups |
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1. C*-algebras. (1h) a. Morphism of C*-algebras; b. C*-algebras generated by affiliated elements; c. W*-algebras. 2. Locally compact quantum groups.(1h) a. Compact quantum groups of Woronowicz; b. From multiplicative unitary to locally compact quantum groups; c. Locally compact quantum groups of Kustermans and Vaes. 3. Rieffel Deformation.(3h) a. Rieffel Deformation of C*-algebras; b. Rieffel Deformation of locally compact groups; c. Heisenberg-Lorentz quantum group; d. The second example of quantum Lorentz group obtained by Rieffel Deformation. 4. Quantum codouble.(2h) a. Quantum Lorentz group having Gauss decomposition property; b. Quantum Lorentz group having Iwasawa decomposition property. |
Martin Reuter: Asymptotic Safety in Quantum Einstein Gravity |
| The basic ideas of the Wilsonian renormalization group and its continuum implementation in terms of the effective average action are reviewed and its application to Quantum Einstein Gravity (QEG) is discussed. This approach is used then to explore the nonperturbative renormalizability (asymptotic safety) of QEG and the fractal-like nature of its effective spacetimes. |
Jean-Marc Schlenker: Hyperbolic geometry for 3d gravity |
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- hyperbolic surfaces, complex surfaces, Teichmüller space - quadratic holomorphic differentials as the cotangent of Teichmüller space - measured geodesic lamination as another description of the cotangent of Teichmüller - Thurston's Earthquake theorem - quasifuchsian 3-dim hyperbolic manifolds, the Ahlfors-Bers theorem - 3-dim GHMC AdS manifolds - the Mess proof of the earthquake theorem through GHMC AdS manifolds. |
Ruth Williams: Introduction to Regge calculus |
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1. Basic formalism; simplex practicalities; Bianchi identities; existence of diffeomorphisms; continuum limit. 2. Regge calculus in 2 dimensions. Regge calculus in 3 dimensions; inclusion of matter; 2+1 Regge calculus and 't Hooft's approach. 3+1 Regge calculus; Sorkin evolution; Lund-Regge approach. 3. Regge calculus in 4 dimensions; weak field calculations; simplicial minisuperspace and quantum cosmology; numerical simulations of discrete quantum gravity; matter; the measure. 4. Regge calculus in a large number of dimensions. Area Regge calculus; motivation and problems; constraints; treating areas as basic variables; discontinous metrics. |
Thomas Thiemann: Loop Quantum Gravity |
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LQG I: Dirac algorithm, Dirac observables, canonical quantisation with constraints LQG II: ADM formulation of GR LQG III: Connection formulation LQG IV: Holonomy flux algebra and its automorphisms LQG V: Ashtekar-Isham-Lewandowski representation A. Existence B. Uniqueness C. Irreducibility LQG VI: Spin network basis, area and volume operators, solutions of Gauss and spatial diffeomorphism constraint LQG VII: Semiclassical kinematical states LQG VIII: Master constraint programme A. Motivation B. Heuristic explanation of UV finiteness in LQG C. Definition of Master constraint operator for geometry and matter, self-adjointness LQG IX: Solution of Master constraint, physical inner product, semiclassical analysis of LQG LQG X: Relation between Spin foam models and Master constraint programme LQG XI: Quantum black hole physics LQG XII: Discussion, examples, toy models, open problems |