Quantum Geometry - A Statistical Field Theory Approach

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.

List 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.

Summary

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.

Product details

• Authors: Jan Ambjorn, Jan Ambjørn, Jan Ambjrn, Bergfinnur Durhuus, Durhuus Bergfinnur, Thordur Jonsson, Jonsson Thordur
• Publisher: Cambridge Academic
• Languages: English
• Product format: Hardback
• Released: 19.06.1997
• EAN: 9780521461672
• ISBN: 978-0-521-46167-2
• Dimensions: 182 mm x 256 mm x 26 mm
• Weight: 835 g
• Illustrations: 73 b/w illus., Zeichnungen, nicht spezifiziert
• Series: Cambridge Monographs on Mathem; Cambridge Monographs on Mathematical Physics
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Theoretical physics; Non-fiction book > Nature, technology > Astronomy: general, reference works; SCIENCE / Physics / General, Physics