Quantum Gravity in 2+1 DimensionsCambridge University Press, 04.12.2003 - 292 Seiten This timely volume provides a broad survey of (2+1)-dimensional quantum gravity. It emphasises the 'quantum cosmology' of closed universes and the quantum mechanics of the (2+1)-dimensional black hole. It compares and contrasts a variety of approaches, and examines what they imply for a realistic theory of quantum gravity. General relativity in three spacetime dimensions has become a popular arena in which to explore the ramifications of quantum gravity. As a diffeomorphism-invariant theory of spacetime structure, this model shares many of the conceptual problems of realistic quantum gravity. But it is also simple enough that many programs of quantization can be carried out explicitly. After analysing the space of classical solutions, this book introduces some fifteen approaches to quantum gravity - from canonical quantization in York's 'extrinsic time' to Chern-Simons quantization, from the loop representation to covariant path integration to lattice methods. Relationships among quantizations are explored, as well as implications for such issues as topology change and the 'problem of time'. This book is an invaluable resource for all graduate students and researchers working in quantum gravity. |
Inhalt
Why 2+1dimensional gravity? | 1 |
11 General relativity in 2+1 dimensions | 3 |
12 Generalizations | 6 |
13 A note on units | 7 |
Classical general relativity in 2+1 dimensions | 9 |
22 The ADM decomposition | 12 |
23 Reduced phase space and moduli space | 15 |
24 Diffeomorphisms and conserved charges | 20 |
84 Perturbation theory | 140 |
Lorentzian path integrals | 143 |
92 Covariant metric path integrals | 149 |
93 Path integrals and firstorder quantization | 152 |
94 Topological field theory | 158 |
Euclidean path integrals and quantum cosmology | 163 |
101 Real tunneling geometries | 164 |
102 The HartleHawking wave function | 165 |
25 The firstorder formalism | 25 |
26 Boundary terms and the WZW action | 29 |
27 Comparing generators of invariances | 34 |
A field guide to the 2+1dimensional spacetimes | 38 |
32 The 2+1dimensional black hole | 45 |
33 The torus universe | 50 |
34 Other topologies | 57 |
Geometric structures and ChernSimons theory | 60 |
42 Geometric structures | 64 |
43 The space of Lorentzian structures | 67 |
44 Adding a cosmological constant | 69 |
45 Closed universes as quotient spaces | 71 |
46 Fiber bundles and flat connections | 77 |
47 The Poisson algebra of the holonomies | 80 |
Canonical quantization in reduced phase space | 87 |
52 Quantization of the reduced phase space | 89 |
53 Automorphic forms and Maass operators | 93 |
54 A general ADM quantization | 96 |
55 Pros and cons | 97 |
The connection representation | 100 |
62 Quantizing geometric structures | 104 |
63 Relating quantizations | 106 |
64 Ashtekar variables | 112 |
65 More pros and cons | 114 |
Operator algebras and loops | 117 |
71 The operator algebra of Nelson and Regge | 118 |
72 The connection representation revisited | 122 |
73 The loop representation | 124 |
The WheelerDeWitt equation | 131 |
81 The firstorder formalism | 132 |
82 A quantum Legendre transformation | 134 |
83 The secondorder formalism | 135 |
103 The sum over topologies | 168 |
Lattice methods | 171 |
111 Regge calculus | 172 |
112 The TuraevViro model | 176 |
113 A Hamiltonian lattice formulation | 183 |
114 t Hoofts polygon model | 186 |
115 Dynamical triangulation | 191 |
The 2+1dimensional black hole | 194 |
121 A brief introduction to black hole thermodynamics | 195 |
122 The Lorentzian black hole | 196 |
123 The Euclidean black hole | 202 |
124 Black hole statistical mechanics | 209 |
Next steps | 212 |
The topology of manifolds | 217 |
A2 The mapping class group | 218 |
A3 Connected sums | 219 |
A4 The fundamental group | 220 |
A5 Covering spaces | 222 |
A6 Quotient spaces | 224 |
A7 Geometrization | 226 |
A8 Simplices and Euler numbers | 227 |
topology of surfaces | 229 |
Lorentzian metrics and causal structure | 236 |
B2 Lorentz cobordism | 239 |
B3 Closed timelike curves and causal structure | 240 |
Differential geometry and fiber bundles | 243 |
C2 Holonomy and curvature | 245 |
C3 Frames and spin connections | 246 |
C5 Fiber bundles and connections | 247 |
References | 250 |
267 | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
2+1 dimensions 2+1)-dimensional black hole 2+1)-dimensional gravity action ADM formalism algebra amplitude analogous anti-de Sitter Ashtekar boundary terms bundle canonical quantization Carlip chapter Chern-Simons theory choice classical computation conjugate connection representation coordinate corresponding cosmological constant covariant covering space curves d²x defined degrees of freedom derivative determined diffeomorphisms dimensional dynamics edges Einstein entropy equivalent Euclidean Euler number field equations field theory flat connections fundamental group gauge-fixing genus g geometric structures geometry Grav Hamiltonian constraint Hilbert space holonomies inner product invariant lattice Lorentzian metric manifold mapping class group moduli space momenta momentum obtain operator path integral phase space Phys physical Poisson brackets polygon quantum field quantum gravity quantum mechanics quantum theory quotient space reduced phase space Regge shown slice solutions spacelike spacetime spin connection surface three-dimensional three-manifold time-slicing topology torus triangulation Turaev-Viro vanishes variables wave function Wheeler-DeWitt equation
Verweise auf dieses Buch
Generalized Analytic Automorphic Forms in Hypercomplex Spaces Rolf S. Krausshar Eingeschränkte Leseprobe - 2004 |
The Structural Foundations of Quantum Gravity Dean Rickles,Steven French,Juha T. Saatsi Keine Leseprobe verfügbar - 2006 |