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By Thomas Thiemann
Publisher: Cambridge University Press
Print Publication Year:2007
Online Publication Date:August 2010
Online ISBN:9780511755682
Hardback ISBN:9780521842631
Paperback ISBN:9780521741873
Book DOI: http://dx.doi.org/10.1017/CBO9780511755682
Subjects: Cosmology, Relativity and Gravitation , Theoretical Physics and Mathematical Physics
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.
Reviews:
pp. i-viii
pp. ix-xvi
Foreword, by Chris Isham: Read PDF
pp. xvii-xviii
pp. xix-xxii
Notation and conventions: Read PDF
pp. xxiii-xxvi
Introduction: Defining quantum gravity: Read PDF
pp. 1-36
I - CLASSICAL FOUNDATIONS, INTERPRETATION AND THE CANONICAL QUANTISATION PROGRAMME: Read PDF
pp. 37-38
1 - Classical Hamiltonian formulation of General Relativity: Read PDF
pp. 39-73
2 - The problem of time, locality and the interpretation of quantum mechanics: Read PDF
pp. 74-106
3 - The programme of canonical quantisation: Read PDF
pp. 107-117
4 - The new canonical variables of Ashtekar for General Relativity: Read PDF
pp. 118-138
II - FOUNDATIONS OF MODERN CANONICAL QUANTUM GENERAL RELATIVITY: Read PDF
pp. 139-140
pp. 141-156
6 - Step I: the holonomyâ€“flux algebra P: Read PDF
pp. 157-205
7 - Step II: quantum *-algebra A: Read PDF
pp. 206-211
8 - Step III: representation theory of A: Read PDF
pp. 212-263
9 - Step IV: (1) implementation and solution of the kinematical constraints: Read PDF
pp. 264-278
10 - Step IV: (2) implementation and solution of the Hamiltonian constraint: Read PDF
pp. 279-344
11 - Step V: semiclassical analysis: Read PDF
pp. 345-396
III - PHYSICAL APPLICATIONS: Read PDF
pp. 397-398
12 - Extension to standard matter: Read PDF
pp. 399-430
13 - Kinematical geometrical operators: Read PDF
pp. 431-457
14 - Spin foam models: Read PDF
pp. 458-510
15 - Quantum black hole physics: Read PDF
pp. 511-561
16 - Applications to particle physics and quantum cosmology: Read PDF
pp. 562-571
17 - Loop Quantum Gravity phenomenology: Read PDF
pp. 572-574
IV - MATHEMATICAL TOOLS AND THEIR CONNECTION TO PHYSICS: Read PDF
pp. 575-576
18 - Tools from general topology: Read PDF
pp. 577-584
19 - Differential, Riemannian, symplectic and complex geometry: Read PDF
pp. 585-626
20 - Semianalytic category: Read PDF
pp. 627-633
21 - Elements of fibre bundle theory: Read PDF
pp. 634-643
22 - Holonomies on non-trivial fibre bundles: Read PDF
pp. 644-651
23 - Geometric quantisation: Read PDF
pp. 652-670
24 - The Dirac algorithm for field theories with constraints: Read PDF
pp. 671-679
25 - Tools from measure theory: Read PDF
pp. 680-688
26 - Key results from functional analysis: Read PDF
pp. 689-700
27 - Elementary introduction to Gel'fand theory for Abelian C*-algebras: Read PDF
pp. 701-712
28 - Bohr compactification of the real line: Read PDF
pp. 713-718
29 - Operator *-algebras and spectral theorem: Read PDF
pp. 719-728
30 - Refined algebraic quantisation (RAQ) and direct integral decomposition (DID): Read PDF
pp. 729-745
31 - Basics of harmonic analysis on compact Lie groups: Read PDF
pp. 746-754
32 - Spin-network functions for SU(2): Read PDF
pp. 755-769
33 - + Functional analytic description of classical connection dynamics: Read PDF
pp. 770-774
pp. 775-808
pp. 809-819