Heat Kernels and Dirac Operators

The first edition of this book presented 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), 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 softcover. 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.

Product details

• Authors: Nicole Berline, Ezra Getzler, Michèle Vergne
• Publisher: Springer, Berlin
• Content: Book
• Product form: Paperback / Softback
• Publication date: 01.01.2003
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Geometry
• EAN: 9783540200628
• ISBN: 978-3-540-20062-8
• Pages: 363
• Illustrations: IX, 363 p.
• Dimensions (packing): 15.6 x 23.7 x 2.1 cm
• Weight (packing): 580 g
• Series: Grundlehren Text Editions
• Subjects: B, Mathematische Physik, Differenzialgeometrie, Geometrie / Differenzialgeometrie, Gruppen und Gruppentheorie, Group Theory, Physics, Mathematics and Statistics, Theoretical, Mathematical and Computational Physics, Differential Geometry, Mathematical physics, Groups & group theory, Group Theory and Generalizations, Numerical and Computational Physics, Simulation, Mathematical Methods in Physics, YellowSale2006, Mathematische / Computergestützte / Theoretische Physik, 58A10, 58G11, 58G10, Superconnections, Diracoperators, 53C05, HeatKernelDifferentialGeometry, Atiyah-Singerindextheorem