Quantum Gravity in 2+1 Dimensions

by Steven Carlip

• ISBN13: 9780521545884
• ISBN10: 0521545889
• Format: Paperback
• Copyright: 2003-12-04
• Publisher: Cambridge University Press

Summary

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.

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.