1. Loop Quantum Gravity and Recent Progress Yi Ling (凌 意） ITP, Chinese Academy of Sciences Dec.27, 2003

2. Loop Quantum Gravity and Recent Progress • Brief history of loop quantum gravity • Ashtekar-Sen variables • Spin networks • Applications and recent progress • Isolated horizon and entropy of black holes • Loop quantum cosmology • Positive cosmological constant and Chern-Simons states

3. Einstein’s Dream

4. Quantum mechanics +special relativity Quantum field theory Electromagnetic interaction (QED) Weak interaction Strong interaction (QCD) Renormalizable • Quantum field theory +general relativity Quantum gravity Gravitational interaction Non-renormalizable

5. Advices From Dirac • How then do they manage with these incorrect equation? These equations lead to infinities when one tries to solve them; These infinities ought not to be there. They remove them artificially… ------ The inadequacies of quantum filed theory.

6. General Relativity +Quantum Mechanics

7. General Relativity +Quantum Mechanics • 3+1 decomposition

8. General Relativity +Quantum Mechanics • Wheeler-Dewitt equation

9. Ashtekar-Sen Variables • Ashtekar-Sen variables a: SU(2) index

10. Constraints • 3+1 decomposition

11. SU(2) Diff(M) H ? Solutions to These Equations • Three steps

12. Loop States • Holonomy • Multi-loop states

13. Spin Networks • Spin networks j 1 j 2 v j 1 3

14. Discreteness of Quantum Geometry • Microscopic version of space

15. Discreteness of Quantum Geometry • Area spectrum j

16. Dynamics • Causal spin networks and spin foams t 3 t 2 t 1

17. Recent Progress in Loop Quantum Gravity • Isolated horizons and dynamical black holes • Quantum gravity with positive cosmological constant • The absence of singularity in loop quantum cosmology • Extending it to supergravity and M theory

18. Isolated Horizons and Statistical Entropy of Black Holes • Bekenstein-Hawking entropy

19. A Quick Review on Isolated Horizons • Motivations • Origin of black hole entropy • Physical laws of general black holes The zeroth and first law: Stationary black holes • (Quasi)local quantities on the horizon The mass, angular momentum and charges: Global concepts

20. A Quick Review on Isolated Horizons • Weakly isolated horizons • SO(3) (non-rotating) • Axi-symmetry(rotating) • Distortion • Dynamical horizons

21. Boundary Theory on Isolated Horizons • Self-dual action

22. Boundary Theory on Isolated Horizons • Consequences of boundary conditions on horizon

23. Boundary Theory on Isolated Horizons

24. Boundary Theory on Isolated Horizons • Quantization

25. Boundary Theory on Isolated Horizons • From quantum general relativity • From quantum Chern-Simons theory

26. Boundary Theory on Isolated Horizons • Hilbert space

27. Boundary Theory on Isolated Horizons • Topological quantum field theory

28. Discrete Horizons From Quantum Geometry • The most probable distribution • The area of discrete horizon

29. Counting the Number of Microstates of Quantum Gravity • The entropy of discrete horizon

30. Fixing the Immirzi Parameter • Quasinormal modes of black holes • Bohr’s correspondence principle

31. Fixing the Immirzi Parameter • Quantum GR • Loop quantization of N=1 supergravity

32. Some Progress in Loop Quantum Cosmology • The absence of singularity in loop quantum cosmology Closed universe with k=1, Scale factor Originated from a big-bang

33. Some Progress in Loop Quantum Cosmology Quantum Mechanically We would expect Thus, is a classical relation.

34. Some Progress in Loop Quantum Cosmology Quantum geometry

35. n

36. Some Progress in Loop Quantum Cosmology • Positive cosmological and Chern-Simons states

37. Some Progress in Loop Quantum Cosmology • Kodama state • Problem of time • Energy-momentum relations(Lorentz Violation)

38. M theory Loop Quantum GR String theory D=11 Supergravity D=10 Supergravity D=4,N=1,2 Supergravity D=4,N=8 Supergravity Extend It to supergravity and M Theory

39. Thank You