Loop Spaces Characteristic Classes and Geometric Quantization

This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics.

Loop Spaces  Characteristic Classes and Geometric Quantization

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.

More Books:

Loop Spaces, Characteristic Classes and Geometric Quantization
Language: en
Pages: 302
Authors: Jean-Luc Brylinski
Categories: Mathematics
Type: BOOK - Published: 2009-12-30 - Publisher: Springer Science & Business Media

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,
Loop Spaces, Characteristic Classes and Geometric Quantization
Language: en
Pages: 302
Authors: Jean-Luc Brylinski
Categories: Mathematics
Type: BOOK - Published: 2007-11-15 - Publisher: Springer Science & Business Media

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,
Geometry at the Frontier: Symmetries and Moduli Spaces of Algebraic Varieties
Language: en
Pages: 282
Authors: Paola Comparin, Eduardo Esteves, Herbert Lange, Sebastián Reyes-Carocca, Rubí E. Rodríguez
Categories: Education
Type: BOOK - Published: 2021-04-23 - Publisher: American Mathematical Soc.

Articles in this volume are based on lectures given at three conferences on Geometry at the Frontier, held at the Universidad de la Frontera, Pucón, Chile in 2016, 2017, and 2018. The papers cover recent developments on the theory of algebraic varieties—in particular, of their automorphism groups and moduli spaces.
Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics
Language: en
Pages: 310
Authors: Vincent Guedj
Categories: Mathematics
Type: BOOK - Published: 2012-01-06 - Publisher: Springer Science & Business Media

The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation,
A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds
Language: en
Pages: 140
Authors: Yohann Le Floch
Categories: Mathematics
Type: BOOK - Published: 2018-09-19 - Publisher: Springer

This text provides a comprehensive introduction to Berezin–Toeplitz operators on compact Kähler manifolds. The heart of the book is devoted to a proof of the main properties of these operators which have been playing a significant role in various areas of mathematics such as complex geometry, topological quantum field theory,