Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents(4 chapters)
About this book
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.
Bibliographic Information
Book Title: Geometric and Topological Methods for Quantum Field Theory
Editors: Hernán Ocampo, Sylvie Paycha, Andrés Vargas
Series Title: Lecture Notes in Physics
DOI: https://doi.org/10.1007/b104936
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2005
Hardcover ISBN: 978-3-540-24283-3Published: 13 June 2005
Softcover ISBN: 978-3-642-06351-0Published: 22 October 2010
eBook ISBN: 978-3-540-31522-3Published: 12 May 2005
Series ISSN: 0075-8450
Series E-ISSN: 1616-6361
Edition Number: 1
Number of Pages: XV, 230
Topics: Mathematical Methods in Physics, Quantum Field Theories, String Theory, Elementary Particles, Quantum Field Theory, Manifolds and Cell Complexes (incl. Diff.Topology), Differential Geometry