Modern Canonical Quantum General Relativity

Canonical quantisation and loop quantum gravity theory for graduate students of quantum field theory.

Thomas Thiemann (Author)

9780521741873, Cambridge University Press

Paperback, published 13 November 2008

846 pages
24.8 x 17.4 x 4.6 cm, 1.41 kg

'… 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

Modern physics rests on two fundamental building blocks: general relativity and quantum theory. General relativity is a geometric interpretation of gravity while quantum theory governs the microscopic behaviour of matter. Since matter is described by quantum theory which in turn couples to geometry, we need a quantum theory of gravity. In order to construct quantum gravity one must reformulate quantum theory on a background independent way. Modern Canonical Quantum General Relativity provides a complete treatise of the canonical quantisation of general relativity. The focus is on detailing the conceptual and mathematical framework, on describing physical applications and on summarising the status of this programme in its most popular incarnation, called loop quantum gravity. Mathematical concepts and their relevance to physics are provided within this book, which therefore can be read by graduate students with basic knowledge of quantum field theory or general relativity.

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.

Subject Areas: Relativity physics [PHR], Physics [PH], Cosmology & the universe [PGK], Mathematics [PB]