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Quantum Geometry : A Statistical Field Theory Approach - Jan Ambjorn

Quantum Geometry

A Statistical Field Theory Approach


Published: 18th August 2010
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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.

"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

Introductionp. 1
Random walksp. 11
Random surfacesp. 66
Two-dimensional gravityp. 149
Monte Carlo simulations of random geometryp. 251
Gravity in higher dimensionsp. 271
Topological quantum field theoriesp. 297
Referencesp. 339
Indexp. 359
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780521461672
ISBN-10: 0521461677
Series: Cambridge Monographs on Mathematical Physics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 380
Published: 18th August 2010
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.7 x 17.4  x 2.2
Weight (kg): 0.88