Synopses & Reviews
Review
"This book covers a wide range of topics in classical and quantum gravity in three spacetime dimensions. In the process, it also discusses the main conceptual and technical issues associated with quantization of generally covariant theories...a good, self-contained introduction to many topics in quantum gravity..." Mathematical Reviews
Review
'For both experts and non-experts, this is an eminently readable and useful book.' Renate Loll, General Relativity and Gravitation
Synopsis
The first comprehensive survey of (2+1)-dimensional quantum gravity - for graduate students and researchers.
Synopsis
The first comprehensive survey of (2+1)-dimensional quantum gravity. It presents some fifteen different approaches, comparing the resulting theories and suggesting implications for the ultimate goal of a (3+1)-dimensional theory uniting general relativity and quantum mechanics. An invaluable resource for all graduate students and researchers working in quantum gravity.
Synopsis
A key challenge in modern physics is to combine general relativity (our theory of gravity) and quantum mechanics into a quantum theory of gravity. Since we do not yet have a fully-fledged theory, it is helpful to look at simplified models. (2+1)-dimensional gravity - general relativity in two spatial dimensions plus time - is simple enough that a variety of quantum theories can be written down explicitly. While the resulting models are not physically realistic, they are conceptually close to realistic (3+1)-dimensional gravity, and they can provide us with valuable guidance. This timely volume is the first comprehensive survey of such theories. It presents some fifteen different approaches to (2+1)-dimensional quantum gravity, comparing the resulting theories and suggesting implications for the ultimate goal of finding a (3+1)-dimensional theory. This book is an invaluable resource for all graduate students and researchers working in quantum gravity.
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.