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Geometric and Topological Methods for Quantum Field Theory: Summer School on Geometric and Topological Methods for Quantum Field Theory July 11-29, ... Colombia (Contemporary Mathematics, 434) - Softcover
Synopsis
Based upon lectures and other communications at the July 2005 summer school, this introduces readers to some recent developments in active research on the interface between geometry, topology and quantum field theory. In five survey lectures the contributors cover anomalies and noncommutative geometry, deformation quantization and Poisson algebras, and topological quantum field theory and orbifolds. These are followed by nine cutting-edge articles with topics including n-flat connections, Dirac equations in a black hole background, homological matrices, quantitative properties of stratified flows, property (T) and tensor products by certain irreducible finite dimensional representations, Painleve equations for invariant instantons, quantum statistical mechanics and class field theory, Kashiwara's quantization of complex contact manifolds and K-theoretic labeling for quasicrystals. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)
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Book Description
Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics, including geometric topology, quantum cohomology and noncommutative geometry. It also explores a wide spectrum of topics on the borderline of mathematics and physics.
From the Back Cover
This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.
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