Articoli correlati a Heat Kernels and Dirac Operators: Vol 298
Sinossi
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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Dalla quarta di copertina
In the first edition of this book, simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut) were presented, using an explicit geometric construction of the heat kernel of a generalized Dirac operator; the new edition makes this popular book available to students and researchers in an attractive paperback. The first four chapters could be used as the text for a graduate course on the applications of linear elliptic operators in differential geometry and the only prerequisites are a familiarity with basic differential geometry. The next four chapters discuss the equivariant index theorem, and include a useful introduction to equivariant differential forms. The last two chapters give a proof, in the spirit of the book, of Bismut's Local Family Index Theorem for Dirac operators. This book will be of interest to graduate students and researchers in differential geometry, Arakelov geometry, group representation theory and mathematical physics.
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Heat Kernels and Dirac Operators (Grundlehren der mathematischen Wissenschaften)
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Heat Kernels and Dirac Operators (Grundlehren der mathematischen Wissenschaften) Berline, Nicole, Ezra Getzler Michèle Vergne a. o.
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