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Dirac Operators and Spectral Geometry

1998-08-20 Mathematics
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Release : 1998-08-20
Genre : Mathematics
Kind : eBook
Book Rating : 629/5 ( reviews)

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Book Synopsis Dirac Operators and Spectral Geometry by : Giampiero Esposito

Download or read book Dirac Operators and Spectral Geometry written by Giampiero Esposito. This book was released on 1998-08-20. Available in PDF, EPUB and Kindle. Book excerpt: A clear, concise and up-to-date introduction to the theory of the Dirac operator and its wide range of applications in theoretical physics for graduate students and researchers.

The Dirac Spectrum

2009-06-11 Mathematics
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Release : 2009-06-11
Genre : Mathematics
Kind : eBook
Book Rating : 697/5 ( reviews)

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Book Synopsis The Dirac Spectrum by : Nicolas Ginoux

Download or read book The Dirac Spectrum written by Nicolas Ginoux. This book was released on 2009-06-11. Available in PDF, EPUB and Kindle. Book excerpt: This volume surveys the spectral properties of the spin Dirac operator. After a brief introduction to spin geometry, we present the main known estimates for Dirac eigenvalues on compact manifolds with or without boundaries. We give examples where the spectrum can be made explicit and present a chapter dealing with the non-compact setting. The methods mostly involve elementary analytical techniques and are therefore accessible for Master students entering the subject. A complete and updated list of references is also included.

Heat Kernels and Dirac Operators

2003-12-08 Mathematics
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Release : 2003-12-08
Genre : Mathematics
Kind : eBook
Book Rating : 628/5 ( reviews)

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Book Synopsis Heat Kernels and Dirac Operators by : Nicole Berline

Download or read book Heat Kernels and Dirac Operators written by Nicole Berline. This book was released on 2003-12-08. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Dirac Operators on Manifolds

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 652/5 ( reviews)

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Book Synopsis An Introduction to Dirac Operators on Manifolds by : Jan Cnops

Download or read book An Introduction to Dirac Operators on Manifolds written by Jan Cnops. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The chapters on Clifford algebra and differential geometry can be used as an introduction to the topics, and are suitable for senior undergraduates and graduates. The other chapters are also accessible at this level.; This self-contained book requires very little previous knowledge of the domains covered, although the reader will benefit from knowledge of complex analysis, which gives the basic example of a Dirac operator.; The more advanced reader will appreciate the fresh approach to the theory, as well as the new results on boundary value theory.; Concise, but self-contained text at the introductory grad level. Systematic exposition.; Clusters well with other Birkhäuser titles in mathematical physics.; Appendix. General Manifolds * List of Symbols * Bibliography * Index

Dirac Operators in Riemannian Geometry

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 802/5 ( reviews)

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Book Synopsis Dirac Operators in Riemannian Geometry by : Thomas Friedrich

Download or read book Dirac Operators in Riemannian Geometry written by Thomas Friedrich. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: Examines the Dirac operator on Riemannian manifolds, especially its connection with the underlying geometry and topology of the manifold. The presentation includes a review of Clifford algebras, spin groups and the spin representation, as well as a review of spin structures and spin [superscript C] structures. With this foundation established, the Dirac operator is defined and studied, with special attention to the cases of Hermitian manifolds and symmetric spaces. Then, certain analytic properties are established, including self-adjointness and the Fredholm property. An important link between the geometry and the analysis is provided by estimates for the eigenvalues of the Dirac operator in terms of the scalar curvature and the sectional curvature. Considerations of Killing spinors and solutions of the twistor equation on M lead to results about whether M is an Einstein manifold or conformally equivalent to one. Finally, in an appendix, Friedrich gives a concise introduction to the Seiberg-Witten invariants, which are a powerful tool for the study of four-manifolds. There is also an appendix reviewing principal bundles and connections.

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