Quantum Geometry
A Statistical Field Theory Approach

Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.

Jan Ambjørn (Author), Bergfinnur Durhuus (Author), Thordur Jonsson (Author)

9780521017367, Cambridge University Press

Paperback, published 15 December 2005

380 pages, 73 b/w illus.
24.5 x 17 x 2 cm, 0.593 kg

"It was a pleasure to look through this book. It is apparent that every effort was made to write a complete advanced text on the current status of triangulations in quantum gravity. This book is a must for anyone in this field." E. J. Janse van Rensburg, Mathematical Reviews

This graduate/research level text describes in a unified fashion the statistical mechanics of random walks, random surfaces and random higher dimensional manifolds with an emphasis on the geometrical aspects of the theory and applications to the quantisation of strings, gravity and topological field theory. With chapters on random walks, random surfaces, two- and higher dimensional quantum gravity, topological quantum field theories and Monte Carlo simulations of random geometries, the text provides a self-contained account of quantum geometry from a statistical field theory point of view. The approach uses discrete approximations and develops analytical and numerical tools. Continuum physics is recovered through scaling limits at phase transition points and the relation to conformal quantum field theories coupled to quantum gravity is described. The most important numerical work is covered, but the main aim is to develop mathematically precise results that have wide applications. Many diagrams and references are included.

Preface
1. Introduction
2. Random walks
3. Random surfaces
4. Two-dimensional gravity
5. Monte Carlo simulations
6. Gravity in higher dimensions
7. Topological quantum field theories
References
Index.

Subject Areas: Physics [PH]