Geometric and Topological Methods for Quantum Field Theory - Hardcover

Hardcover

ISBN 10: 0521764823 ISBN 13: 9780521764827

Publisher: Cambridge University Press, 2010

Synopsis

Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.

About this title

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2010
• ISBN 10: 0521764823
• ISBN 13: 9780521764827
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 434
• Editor: Ocampo Hernan, Pariguan Eddy, Paycha Sylvie