
Heat Kernels and Dirac Operators
Springer (Publisher)
199th Edition
Published in 1996
Book
Hardback
VII, 369 pages
978-3-540-53340-5 (ISBN)
Description
The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recent generalizations, are presented. The formula for the index of the Dirac operator is obtained from the classical formula for the heat kernel of the harmonic oscillator. The only prerequisite to reading this book is a familiarity with basic differential geometry. There are several chapters of preparatory material, including a treatment of connections and Quillen's theory of superconnections, characteristic classes, the theory of the heat equation and its solution on a compact manifold, Clifford algebras, Dirac operators and equivariant differential forms. The book finishes with a treatment of the index bundle and Bismut's local version of the Atiyah-Singer Index Theorem for families. As an application, the curvature of the determinant line bundle is calculated, following Bismut and Freed.
More details
Series
Edition
199., Corr. 2nd printing
Language
English
Place of publication
Berlin
Germany
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 216 mm
Width: 138 mm
Weight
690 gr
ISBN-13
978-3-540-53340-5 (9783540533405)
Schweitzer Classification
Other editions
Additional editions

Nicole Berline | Ezra Getzler | Michèle Vergne
Heat Kernels and Dirac Operators
Book
12/2003
Springer
€69.54
Shipment within 10-15 days