TY  - BOOK
AU  - 
AU  - 
AU  - 
ED  - SpringerLink (Online service)
TI  - Geometric and Topological Methods for Quantum Field Theory
T2  - Lecture Notes in Physics,
SN  - 9783540315223
AV  - QC5.53 
U1  - 530.15 23
PY  - 2005///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Physics
KW  - Global differential geometry
KW  - Cell aggregation
KW  - Mathematics
KW  - Mathematical physics
KW  - Quantum theory
KW  - Mathematical Methods in Physics
KW  - Physics beyond the Standard Model
KW  - Elementary Particles, Quantum Field Theory
KW  - Manifolds and Cell Complexes (incl. Diff.Topology)
KW  - Differential Geometry
N1  - Knot Invariants and Configuration Space Integrals (Christine Lescop) -- Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces (Raimar Wulkenhaar) -- Introduction to String Compactification (Anamaria Font, Stefan Theisen) -- Index Theorems and Noncommutative Topology (Thierry Fack); ZDB-2-PHA; ZDB-2-LNP
N2  - 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
UR  - http://dx.doi.org/10.1007/b104936
ER  -