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.
Canonical quantisation and loop quantum gravity theory for graduate students of quantum field theory.
Thomas Thiemann is Staff Scientist at the Max Planck Institut fur 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-Westfalisch 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.
'... the most complete account to date of the Hamiltonian approach to the quantization of General Relativity. ... If the exciting possibility of links ... between words of the very small and the very large are realized, then theorists will have to delve much deeper into the structure of quantum gravity than hitherto. This book is a magnificent and comprehensive introduction to one possible avenue. It has no rival.' The Observatory