Dirac Operators and Spectral Geometry PDF Download

Author: Giampiero Esposito
Publisher: Cambridge University Press
ISBN: 0521648629
Category : Mathematics
Languages : en
Pages : 227

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Book Description
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.

Author: Nicolas Ginoux
Publisher: Springer
ISBN: 3642015700
Category : Mathematics
Languages : en
Pages : 168

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Book Description
This volume surveys the spectral properties of the spin Dirac operator. After a brief introduction to spin geometry, it presents the main known estimates for Dirac eigenvalues on compact manifolds with or without boundaries.

Author: Nicole Berline
Publisher: Springer Science & Business Media
ISBN: 9783540200628
Category : Mathematics
Languages : en
Pages : 384

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Book Description
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.

Author: Steen Markvorsen
Publisher: Birkhäuser
ISBN: 3034880553
Category : Mathematics
Languages : en
Pages : 96

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Book Description
This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.

Author: Jing-Song Huang
Publisher: Springer Science & Business Media
ISBN: 0817644938
Category : Mathematics
Languages : en
Pages : 205

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Book Description
This book presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. The book is an excellent contribution to the mathematical literature of representation theory, and this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.

Author: Pierre H. Berard
Publisher: Springer
ISBN: 3540409580
Category : Mathematics
Languages : en
Pages : 284

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Book Description

Author: Richard Melrose
Publisher: CRC Press
ISBN: 1439864608
Category : Mathematics
Languages : en
Pages : 392

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Book Description
Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.

Author: Peter B. Gilkey
Publisher: CRC Press
ISBN: 1135440743
Category : Mathematics
Languages : en
Pages : 315

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Book Description
A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. Written by a leading pioneer in the field, it focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation. It incorporates the work of many authors into the presentation, and includes a complete bibliography that serves as a roadmap to the literature on the subject. Geometers, mathematical physicists, and analysts alike will undoubtedly find this book to be the definitive book on the subject

Author: Thomas Friedrich
Publisher: American Mathematical Soc.
ISBN: 0821820559
Category : Mathematics
Languages : en
Pages : 213

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Book Description
For a Riemannian manifold M, the geometry, topology and analysis are interrelated in ways that have become widely explored in modern mathematics. Bounds on the curvature can have significant implications for the topology of the manifold. The eigenvalues of the Laplacian are naturally linked to the geometry of the manifold. For manifolds that admit spin structures, one obtains further information from equations involving Dirac operators and spinor fields. In the case of four-manifolds, for example, one has the remarkable Seiberg-Witten invariants. In this text, Friedrich 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 $\textrm{spin}mathbb{C}$ 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. This detailed book with elegant proofs is suitable as a text for courses in advanced differential geometry and global analysis, and can serve as an introduction for further study in these areas. This edition is translated from the German edition published by Vieweg Verlag.

Author: Dmitri Fursaev
Publisher: Springer Science & Business Media
ISBN: 9400702051
Category : Science
Languages : en
Pages : 294

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Book Description
This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.