Modern Canonical Quantum General Relativity (Cambridge Monographs on Mathematical Physics)
Cambridge University Press, 11/13/2008
EAN 9780521741873, ISBN10: 0521741874
Paperback, 846 pages, 24.8 x 17.4 x 4.6 cm
Language: English
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.