Quantum Geometry: A Statistical Field Theory Approach

Quantum Geometry: A Statistical Field Theory Approach

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Cambridge University Press

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Quantum Geometry: A Statistical Field Theory Approach

This graduate 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 quantization 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.

Product Details

ISBN-13: 9780521461672
Publisher: Cambridge University Press
Publication date: 09/01/1997
Series: Cambridge Monographs on Mathematical Physics Series
Pages: 380
Product dimensions: 6.85(w) x 9.72(h) x 0.87(d)

Table of Contents

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.

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