This timely volume provides a broad survey of (2+1)-dimensional quantum gravity. It emphasizes 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 analyzing 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. It also explores relationships among quantizations, and 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.
