Modern Canonical Quantum General Relativity Book

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.