Loop Spaces, Characteristic Classes and Geometric Quantization
Loop Spaces, Characteristic Classes and Geometric Quantization (Modern Birkhäuser Classics)Jean-Luc Brylinski,
Publisher: Birkhäuser Boston
ISBN: 0817647309 ISBN13: 9780817647308 DDC: 516 Edition: Paperback; 2007-11-15
Summary:
This book deals with the differential geometry of manifolds, loopspaces, line bundles and groupoids, and the relations of this
geometry to mathematical physics. Various developments in
mathematical physics (e.g., in knot theory, gauge theory, and
topological quantum field theory) have led mathematicians and
physicists to search for new geometric structures on manifolds and to
seek a synthesis of ideas from geometry, topology and category
theory. In this spirit, this book develops the differential geometry
associated to the topology and obstruction theory of certain fiber
bundles (more precisely, associated to grebes). The theory is a
3-dimensional analog of the familiar Kostant--Weil theory of line
bundles. In particular the curvature now becomes a 3-form.
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, Cheeger--Chern--Simons
secondary characteristics classes, and group cohomology. Finally, the
last chapter deals with the Dirac monopole and Dirac’s quantization
of the electrical charge. The book will be of interest to
topologists, geometers, Lie theorists and mathematical physicists, as
well as to operator algebraists. It is written for graduate students
and researchers, and will be an excellent textbook. It has a
self-contained introduction to the theory of sheaves and their
cohomology, line bundles and geometric prequantization à la
Kostant--Souriau.
Classification: |
(click to see other 'Books on the Same Shelf') |
Book Details:
Physical Description: 6.1"x9.1"x0.4"; 1.0 lb; 302 pagesEdition Info: Paperback; 2007-11-15
Similar Books:
| • | Algebraic K-Theory (V. Srinivas, ; ISBN: 0817647368; Paperback; 2007-11-13; 93% match) |
| • | Geometry and Dynamics of Groups and Spaces: In Memory of Alexander Reznikov (Mikhail Kapranov (Editor), Sergiy Kolyada (Editor), Yuri I. Manin (Editor), Pieter Moree (Editor), Leonid Potyagailo (Editor); ISBN: 376438607X; Hardcover; 2008-02-06; 89% match) |
| • | Families of Conformally Covariant Differential Operators, Q-Curvature and Holography (Andreas Juhl, ; ISBN: 376439899X; Hardcover; 2009-06-26; 70% match) |
| • | ...more similar books |
Subjects:
Click on a subject to see other books listed with the same subject or to drill down into components of the subject -- such as geographical locations, dates and so on.Buying this book:
We query many merchants so that you can instantly compare prices and availability. You can even check historic prices and subscribe for notifications. For a manual check, clicking on a link will open a new window with a search for this book on the merchant's site of your choice.| • | Amazon.com by title or by ISBN — widest selection, reliable service, good prices |
| • |
Abebooks.com by title or
by ISBN
— good source for rare and out-of-print books
|
| • | Textbooks.com by title or by ISBN — large inventory of new & used textbooks |
| • | Alibris.com by title or by ISBN — their slogan is "books you thought you'd never find" |
| • |
eCampus.com by title or
by ISBN
— they specialize in textbooks, used and new
|
| • | BN.com by title or by ISBN — Barnes & Noble has a wide selection of new and used books |