Modern Canonical Quantum General Relativity
$82.99 (C)
Part of Cambridge Monographs on Mathematical Physics
 Author: Thomas Thiemann, MaxPlanckInstitut für Gravitationsphysik, Germany
 Date Published: December 2008
 availability: Temporarily unavailable  available from TBC
 format: Paperback
 isbn: 9780521741873
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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.
Read more Discusses all aspects of theory from the foundations to the frontiers of current research
 Contains mathematical precision which reaches new levels of rigour
 Designed to be an absolute reference text on the subject
Reviews & endorsements
"This book is a complete treatise on one approach, loop quantum gravity, to reformulating quantum theory in a backgroundindependent way. It is suitable for graduate students and researchers in theoretical physics with a basic knowledge of quantum field theory and general relativity. Dr. Thiemann brings a deep level of mathematical understanding to the problem and has succeeded in solving some of the most complex problems in the area. The book is a snapshot of the theories in the field that may be leading to a greater understanding of our world.
BooksOnLineSee more reviews"I enjoyed the book very much. The reader who is not mathematically oriented may be worried by some of the parts of the book that are more formal. But Thiemann has a careful writing style in which mathematics is used only as much as needed and always after proper definitions. ... I am convinced the book will immediately become a reference on the subject of loop quantum gravity and its modern developments."  Jorge A. Pullin, Mathematical Reviews
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×Product details
 Date Published: December 2008
 format: Paperback
 isbn: 9780521741873
 length: 846 pages
 dimensions: 248 x 174 x 46 mm
 weight: 1.41kg
 availability: Temporarily unavailable  available from TBC
Table of Contents
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 holonomyflux algebra [P]
7. Step II: quantumalgebra
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 nontrivial 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.
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