Quantum Geometry: A Statistical Field Theory Approach – Niels Bohr Institutet - Københavns Universitet

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Quantum Geometry: A Statistical Field Theory Approach

(Cambridge Monographs on Mathematical Physics) (Hardcover)

Quantum Geometry

Jan Ambjørn, Bergfinnur Durhuus, Thordur Jonsson

Hardcover: 377 pages
Publisher: Cambridge University Press
(19 Jun 1997)
Language: English 
ISBN-10: 0521461677
ISBN-13: 978-0521461672

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.

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