Geometric and Topological Methods for Quantum Field Theory / edited by Hernan Ocampo, Sylvie Paycha, Andrés Vargas.

Format:

Book

Contributor:

Ocampo, Hernan, Editor.

Paycha, Sylvie, Editor.

Vargas, Andrés, Editor.

Series:

Lecture Notes in Physics, 0075-8450 ; 668

Language:

English

Subjects (All):

Physics.

Quantum field theory.

String models.

Particles (Nuclear physics).

Manifolds (Mathematics).

Complex manifolds.

Geometry, Differential.

Mathematical Methods in Physics.

Quantum Field Theories, String Theory.

Elementary Particles, Quantum Field Theory.

Manifolds and Cell Complexes (incl. Diff.Topology).

Differential Geometry.

Local Subjects:

Mathematical Methods in Physics.

Quantum Field Theories, String Theory.

Elementary Particles, Quantum Field Theory.

Manifolds and Cell Complexes (incl. Diff.Topology).

Differential Geometry.

Physical Description:

1 online resource (XV, 230 p.)

Edition:

1st ed. 2005.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005.

Language Note:

English

Summary:

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.

Contents:

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).

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

9783540315223

3540315225

OCLC:

1024261891