Thomas Thiemann is Staff Scientist at the Max Planck Institut für Gravitationsphysik (Albert Einstein Institut), Potsdam, Germany. He is also a long-term researcher at the Perimeter Institute for Theoretical Physics and Associate Professor at the University of Waterloo, Canada. Thomas Thiemann obtained his PhD in theoretical physics from the Rheinisch-Westfälisch Technische Hochschule, Aachen, Germany. He held two year postdoctoral positions at The Pennsylvania State University and Harvard University. As of 2005 he holds a guest professor position at Beijing Normal University, China.
Preface
Notation and conventions
Introduction
Part I. Classical Foundations, Interpretation and the Canonical Quantisation Programme: 1. Classical Hamiltonian formulation of general relativity
2. The problem of time, locality and the interpretation of quantum mechanics
3. The programme of canonical quantisation
4. The new canonical variables of Ashtekar for general relativity
Part II. Foundations of Modern Canonical Quantum General Relativity: 5. Introduction
6. Step I: the holonomy-flux algebra [P]
7. Step II: quantum-algebra
8. Step III: representation theory of [A]
9. Step IV: 1. Implementation and solution of the kinematical constraints
10. Step V: 2. Implementation and solution of the Hamiltonian constraint
11. Step VI: semiclassical analysis
Part III. Physical Applications: 12. Extension to standard matter
13. Kinematical geometrical operators
14. Spin foam models
15. Quantum black hole physics
16. Applications to particle physics and quantum cosmology
17. Loop quantum gravity phenomenology
Part IV. Mathematical Tools and their Connection to Physics: 18. Tools from general topology
19. Differential, Riemannian, symplectic and complex geometry
20. Semianalytical category
21. Elements of fibre bundle theory
22. Holonomies on non-trivial fibre bundles
23. Geometric quantisation
24. The Dirac algorithm for field theories with constraints
25. Tools from measure theory
26. Elementary introduction to Gel'fand theory for Abelean C* algebras
27. Bohr compactification of the real line
28. Operatir -algebras and spectral theorem
29. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID)
30. Basics of harmonic analysis on compact Lie groups
31. Spin network functions for SU(2)
32. + Functional analytical description of classical connection dynamics
Bibliography
Index.
