Lecture Notes On Topological Quantum Field Theories And Geometry Of Loop Spaces
Title | Lecture Notes On Topological Quantum Field Theories And Geometry Of Loop Spaces PDF eBook |
Author | Laszlo Feher |
Publisher | World Scientific |
Pages | 124 |
Release | 1992-10-09 |
Genre | |
ISBN | 9814553956 |
These lectures introduce some very popular fields in topology. The topics discussed are interrelated with modern physics and include works of four leading researchers: M Atiyah, R Bott, J Jones and G Segal. The original lectures presented at the conference at Budapest are enlarged with appendices to make these notes self-contained.
Topological Quantum Field Theories and Geometry of Loop Spaces
Title | Topological Quantum Field Theories and Geometry of Loop Spaces PDF eBook |
Author | László Fehér |
Publisher | |
Pages | 112 |
Release | 1992 |
Genre | |
ISBN |
Topological Quantum Field Theories and Geometry of Loop Spaces
Title | Topological Quantum Field Theories and Geometry of Loop Spaces PDF eBook |
Author | Laszlo Feher |
Publisher | |
Pages | 112 |
Release | 1992 |
Genre | Algebraic topology |
ISBN |
Lecture Notes of the Conference on Topological Quantum Field Theories and Geometry of Loop Spaces
Title | Lecture Notes of the Conference on Topological Quantum Field Theories and Geometry of Loop Spaces PDF eBook |
Author | László Fehér |
Publisher | World Scientific Publishing Company |
Pages | 112 |
Release | 1992 |
Genre | Geometry, Analytic |
ISBN | 9789810211738 |
These lectures introduce some very popular fields in topology. The topics discussed are interrelated with modern physics and include works of four leading researchers: M Atiyah, R Bott, J Jones and G Segal. The original lectures presented at the conference at Budapest are enlarged with appendices to make these notes self-contained.
Loop Spaces, Characteristic Classes and Geometric Quantization
Title | Loop Spaces, Characteristic Classes and Geometric Quantization PDF eBook |
Author | Jean-Luc Brylinski |
Publisher | Springer Science & Business Media |
Pages | 318 |
Release | 2009-12-30 |
Genre | Mathematics |
ISBN | 0817647317 |
This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.
Conformal Field Theory and Topology
Title | Conformal Field Theory and Topology PDF eBook |
Author | Toshitake Kohno |
Publisher | American Mathematical Soc. |
Pages | 188 |
Release | 2002 |
Genre | Mathematics |
ISBN | 9780821821305 |
Geometry and physics have been developed with a strong influence on each other. One of the most remarkable interactions between geometry and physics since 1980 has been an application of quantum field theory to topology and differential geometry. This book focuses on a relationship between two-dimensional quantum field theory and three-dimensional topology which has been studied intensively since the discovery of the Jones polynomial in the middle of the 1980s and Witten's invariantfor 3-manifolds derived from Chern-Simons gauge theory. An essential difficulty in quantum field theory comes from infinite-dimensional freedom of a system. Techniques dealing with such infinite-dimensional objects developed in the framework of quantum field theory have been influential in geometryas well. This book gives an accessible treatment for a rigorous construction of topological invariants originally defined as partition functions of fields on manifolds. The book is organized as follows: The Introduction starts from classical mechanics and explains basic background materials in quantum field theory and geometry. Chapter 1 presents conformal field theory based on the geometry of loop groups. Chapter 2 deals with the holonomy of conformal field theory. Chapter 3 treatsChern-Simons perturbation theory. The final chapter discusses topological invariants for 3-manifolds derived from Chern-Simons perturbation theory.
Geometric And Topological Methods For Quantum Field Theory - Proceedings Of The Summer School
Title | Geometric And Topological Methods For Quantum Field Theory - Proceedings Of The Summer School PDF eBook |
Author | Alexander Cardona |
Publisher | World Scientific |
Pages | 495 |
Release | 2003-03-21 |
Genre | Mathematics |
ISBN | 9814487678 |
This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.