Modern canonical quantum general relativity
 Author/Creator
 Thiemann, Thomas.
 Language
 English.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2007.
 Physical description
 xxvi, 819 p. : ill. ; 26 cm.
 Series
 Cambridge monographs on mathematical physics.
Access
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [775]808) and index.
 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2007
 Responsibility
 Thomas Thiemann.
 Series
 Cambridge monographs on mathematical physics.
 ISBN
 9780521842631
 0521842638