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Quantum field theory

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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.

Geometric quantization. --- Quantum field theory.

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Gauge fields (Physics). --- Mathematical physics. --- Quantum field theory.

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Geometry --- Group theory --- Lie algebras --- Mathematical physics --- Particles (Nuclear physics) --- Quantum field theory

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Quantum mechanics. Quantumfield theory --- Quantum field theory. --- Topology. --- Stochastic geometry. --- Mathematical physics. --- Champs, Théorie quantique relativiste des. --- Topologie. --- Géométrie stochastique. --- Physique mathématique. --- Mathematical physics --- Quantum field theory --- Stochastic geometry --- Topology --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Physical mathematics --- Physics --- Mathematics