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Quantum geometry. A statistical field theory approach. (English) Zbl 0993.82500
Cambridge: Cambridge University Press. 377 p. (1997).
Publisher’s description: 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.

MSC:
82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
82B80 Numerical methods in equilibrium statistical mechanics (MSC2010)
83C45 Quantization of the gravitational field
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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