Quantum Gravity in 2+1 Dimensions
Series: Cambridge Monographs on Mathematical Physics;
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Product details:
- Publisher Cambridge University Press
- Date of Publication 4 December 2003
- ISBN 9780521545884
- Binding Paperback
- No. of pages292 pages
- Size 247x190x18 mm
- Weight 530 g
- Language English
- Illustrations 35 b/w illus. 0
Categories
Short description:
The first comprehensive survey of (2+1)-dimensional quantum gravity - for graduate students and researchers.
MoreLong description:
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.
'For both experts and non-experts, this is an eminently readable and useful book.' Renate Loll, General Relativity and Gravitation
Table of Contents:
1. Why (2+1)-dimensional gravity?; 2. Classical general relativity in 2+1 dimensions; 3. A field guide to the (2+1)-dimensional spacetimes; 4. Geometric structures and Chern-Simons theory; 5. Canonical quantization in reduced phase space; 6. The connection representation; 7. Operator algebras and loops; 8. The Wheeler-DeWitt equation; 9. Lorentzian path integrals; 10. Euclidian path integrals and quantum cosmology; 11. Lattice methods; 12. The (2+1)-dimensional black hole; 13. Next steps; Appendix A. The topology of manifolds; Appendix B. Lorentzian metrics and causal structure; Appendix C. Differential geometry and fiber bundles; References; Index.
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