The Index Formula For Dirac Operators
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The Index Formula For Dirac Operators
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Author : Levi Lopes de Lima
language : en
Publisher:
Release Date : 2003
The Index Formula For Dirac Operators written by Levi Lopes de Lima and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Dirac equation categories.
Heat Kernels And Dirac Operators
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Author : Nicole Berline
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-12-08
Heat Kernels And Dirac Operators written by Nicole Berline and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-08 with Mathematics categories.
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.
Dirac Operators And Spectral Geometry
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Author : Giampiero Esposito
language : en
Publisher: Cambridge University Press
Release Date : 1998-08-20
Dirac Operators And Spectral Geometry written by Giampiero Esposito and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-20 with Mathematics categories.
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.
Manifolds With Cusps Of Rank One
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Author : Werner Müller
language : en
Publisher: Springer
Release Date : 2006-11-15
Manifolds With Cusps Of Rank One written by Werner Müller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The manifolds investigated in this monograph are generalizations of (XX)-rank one locally symmetric spaces. In the first part of the book the author develops spectral theory for the differential Laplacian operator associated to the so-called generalized Dirac operators on manifolds with cusps of rank one. This includes the case of spinor Laplacians on (XX)-rank one locally symmetric spaces. The time-dependent approach to scattering theory is taken to derive the main results about the spectral resolution of these operators. The second part of the book deals with the derivation of an index formula for generalized Dirac operators on manifolds with cusps of rank one. This index formula is used to prove a conjecture of Hirzebruch concerning the relation of signature defects of cusps of Hilbert modular varieties and special values of L-series. This book is intended for readers working in the field of automorphic forms and analysis on non-compact Riemannian manifolds, and assumes a knowledge of PDE, scattering theory and harmonic analysis on semisimple Lie groups.
Dirac Operators In Representation Theory
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Author : Jing-Song Huang
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-27
Dirac Operators In Representation Theory written by Jing-Song Huang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-27 with Mathematics categories.
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.
Generalized Symplectic Geometries And The Index Of Families Of Elliptic Problems
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Author : Liviu I. Nicolaescu
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-09-11
Generalized Symplectic Geometries And The Index Of Families Of Elliptic Problems written by Liviu I. Nicolaescu and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Geometry, Differential categories.
In this work, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family. All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eight symmetries in the real case and two in the complex case).
The Atiyah Patodi Singer Index Theorem
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Author : Richard Melrose
language : en
Publisher: CRC Press
Release Date : 1993-03-31
The Atiyah Patodi Singer Index Theorem written by Richard Melrose and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-31 with Mathematics categories.
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.
Elliptic Boundary Problems For Dirac Operators
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Author : Bernhelm Booß-Bavnbek
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Elliptic Boundary Problems For Dirac Operators written by Bernhelm Booß-Bavnbek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Elliptic boundary problems have enjoyed interest recently, espe cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary. However, the theory of elliptic boundary problems by far has not achieved the same status as the theory of elliptic operators on closed (compact, without boundary) manifolds. The latter is nowadays rec ognized by many as a mathematical work of art and a very useful technical tool with applications to a multitude of mathematical con texts. Therefore, the theory of elliptic operators on closed manifolds is well-known not only to a small group of specialists in partial dif ferential equations, but also to a broad range of researchers who have specialized in other mathematical topics. Why is the theory of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.
An Introduction To Dirac Operators On Manifolds
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Author : Jan Cnops
language : en
Publisher: Birkhauser
Release Date : 2002
An Introduction To Dirac Operators On Manifolds written by Jan Cnops and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Clifford algebras categories.
Dirac operators play an important role in several domains of mathematics and mathematical physics. In this book, the basic theories underlying the concept of Dirac operators are explored. Starting with preliminary material, it covers Clifford algebras, manifolds, conformal maps, unique continuation and the Cauchy kernel, and boundary values. Only real analysis is required, although complex analysis is helpful. Math physicists and theoretical physicists as well as graduate students will find this book a useful resource.
The Localization Problem In Index Theory Of Elliptic Operators
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Author : Vladimir Nazaikinskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-26
The Localization Problem In Index Theory Of Elliptic Operators written by Vladimir Nazaikinskii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-26 with Mathematics categories.
The book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actually a fundamental localization principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of new important problems in index theory. So far, the localization principle has been only scarcely covered in journal papers and not covered at all in monographs. The suggested book is intended to fill the gap. So far, it is the first and only monograph dealing with the topic. Both the general localization principle and its applications to specific problems, existing and new, are covered. The book will be of interest to working mathematicians as well as graduate and postgraduate university students specializing in differential equations and related topics.