The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction -- the direct quantisation of Einstein's general theory of relativity and string theory -- are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantization of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantization, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centres around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantization of black holes, quantum cosmology, the indications of a discrete structure of spacetime, and the origin of irreversibility.The second edition will add some sections on topical issues. These include loop quantum cosmology, dynamical triangulation, renormalization-group approach, primordial black holes, and information-loss problem for black holes. The second edition will also contain some pedagogical extensions. This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science.
Author(s): Claus Kiefer
Series: International Series of Monographs on Physics volume 136
Edition: 2
Publisher: Oxford University Press
Year: 2007
Language: English
Pages: 374
Tags: Физика;Теория относительности и альтернативные теории гравитации;Квантовая гравитация;
Cover......Page 1
Title: Quantum Gravity 2nd Edition By CLAUS KIEFER......Page 4
ISBN: 978–0–19-921252-1......Page 5
PREFACE TO THE SECOND EDITION......Page 6
PREFACE......Page 8
CONTENTS......Page 10
1.1.1 Introduction......Page 14
1.1.2 Main motivations for quantizing gravity......Page 16
1.1.3 Relevant scales......Page 17
1.1.4 Quantum mechanics and Newtonian gravity......Page 20
1.1.5 Quantum field theory in curved space–time......Page 27
1.2 Problems of a fundamentally semiclassical theory......Page 28
1.3 Approaches to quantum gravity......Page 35
2.1.1 Weak gravitational waves......Page 38
2.1.2 Gravitons from representations of the Poincare´ group......Page 43
2.1.3 Quantization of the linear field theory......Page 46
2.2.1 General properties of path integrals......Page 52
2.2.2 The perturbative non-renormalizability......Page 55
2.2.3 Effective action and Feynman rules......Page 60
2.2.4 Semiclassical Einstein equations......Page 68
2.2.5 Asymptotic safety......Page 76
2.2.6 Regge calculus and dynamical triangulation......Page 79
2.3 Quantum supergravity......Page 83
3.1.1 Parametrized non-relativistic particle......Page 86
3.1.2 Some remarks on constrained systems......Page 89
3.1.3 The relativistic particle......Page 91
3.2 The free bosonic string......Page 94
3.3 Parametrized field theories......Page 99
3.4 Relational dynamical systems......Page 106
4.1.1 Principle of path independence......Page 111
4.1.2 Explicit form of generators......Page 113
4.1.3 Geometrodynamics and gauge theories......Page 116
4.2 The 3+1 decomposition of general relativity......Page 118
4.2.1 The canonical variables......Page 119
4.2.2 Hamiltonian form of the Einstein–Hilbert action......Page 122
4.2.3 Discussion of the constraints......Page 127
4.2.4 The case of open spaces......Page 131
4.2.5 Structure of configuration space......Page 133
4.3.1 The canonical variables......Page 137
4.3.2 Discussion of the constraints......Page 140
4.3.3 Loop variables......Page 143
5.1 The programme of canonical quantization......Page 146
5.2 The problem of time......Page 149
5.2.1 Time before quantization......Page 151
5.2.2 Time after quantization......Page 154
5.3.1 The diffeomorphism constraints......Page 157
5.3.2 WKB approximation......Page 160
5.3.3 Remarks on the functional Schrodinger picture......Page 161
5.3.4 Connection with path integrals......Page 164
5.3.5 Anomalies and factor ordering......Page 166
5.3.6 Canonical quantum supergravity......Page 171
5.4.1 Analogies from quantum mechanics......Page 177
5.4.2 Derivation of the Schrodinger equation......Page 183
5.4.3 Quantum-gravitational correction terms......Page 188
6.1.1 Connection representation......Page 194
6.1.2 Loop representation......Page 197
6.2 Quantization of area......Page 202
6.3 Quantum Hamiltonian constraint......Page 207
7.1.1 The laws of black-hole mechanics......Page 212
7.1.2 Hawking and Unruh radiation......Page 214
7.1.3 Bekenstein–Hawking entropy......Page 221
7.2 Canonical quantization of the Schwarzschild black hole......Page 222
7.2.1 Classical formalism......Page 223
7.2.2 Quantization......Page 226
7.3 Black-hole spectroscopy and entropy......Page 230
7.4 Quantum theory of collapsing dust shells......Page 234
7.4.1 Covariant gauge fixing......Page 235
7.4.2 Embedding variables for the classical theory......Page 236
7.4.3 Quantization......Page 239
7.5.1 The classical LTB model......Page 242
7.5.2 Quantization......Page 245
7.6 The information-loss problem......Page 249
7.7 Primordial black holes......Page 251
8.1.1 General introduction......Page 256
8.1.2 Quantization of a Friedmann universe......Page 259
8.1.3 (2+1)-dimensional quantum gravity......Page 269
8.2 Introduction of inhomogeneities......Page 271
8.3 Boundary conditions......Page 275
8.3.2 No-boundary condition......Page 276
8.3.3 Tunnelling condition......Page 281
8.3.4 Comparison of no-boundary and tunnelling wave function......Page 282
8.4.1 Classical variables......Page 285
8.4.2 Quantization......Page 287
9.1 General introduction......Page 292
9.2.1 The Polyakov path integral......Page 297
9.2.2 Effective actions......Page 301
9.2.3 T-duality and branes......Page 304
9.2.4 Superstrings......Page 308
9.2.5 Black-hole entropy......Page 311
9.2.6 Brane worlds......Page 314
10.1 Decoherence and the quantum universe......Page 320
10.1.1 Decoherence in quantum mechanics......Page 321
10.1.2 Decoherence in quantum cosmology......Page 323
10.1.3 Decoherence of primordial fluctuations......Page 331
10.2 Arrow of time......Page 332
10.3 Outlook......Page 337
REFERENCES......Page 340
INDEX......Page 370
