Quantum Geometry A Statistical Field Theory Approach
Quantum Geometry A Statistical Field Theory Approach by Jan Ambjørn is a graduate-level text published by Cambridge University Press on December 15, 2005. This edition spans 380 pages and is presented in English. The book offers a unified exploration of the statistical mechanics of random walks, random surfaces, and higher-dimensional manifolds, focusing on the geometrical aspects of the theory and its applications in string quantization, gravity, and topological field theory.
Readers will find comprehensive chapters covering topics such as random walks, two- and higher-dimensional quantum gravity, and topological quantum field theories, alongside Monte Carlo simulations of random geometries. The text provides a self-contained account of quantum geometry through a statistical field theory lens, utilizing discrete approximations and developing both analytical and numerical tools. It also discusses the recovery of continuum physics through scaling limits at phase transition points and the relationship to conformal quantum field theories coupled to quantum gravity. The book includes numerous diagrams and references to support its mathematical precision and wide-ranging applications.
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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.
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