Heat Kernels And Dirac Operators
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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.
Heat Kernels And Dirac Operators
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Author : Nicole Berline
language : en
Publisher:
Release Date : 2004
Heat Kernels And Dirac Operators written by Nicole Berline and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Differential forms categories.
Heat Kernels And Dirac Operators
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Author : Nicole Berline
language : en
Publisher: Springer Verlag
Release Date : 1992
Heat Kernels And Dirac Operators written by Nicole Berline and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
The Heat Kernel Lefschetz Fixed Point Formula For The Spin C Dirac Operator
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Author : J.J. Duistermaat
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
The Heat Kernel Lefschetz Fixed Point Formula For The Spin C Dirac Operator written by J.J. Duistermaat 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 2013-12-01 with Mathematics categories.
When visiting M.I.T. for two weeks in October 1994, Victor Guillemin made me enthusiastic about a problem in symplectic geometry which involved the use of the so-called spin-c Dirac operator. Back in Berkeley, where I had l spent a sabbatical semester , I tried to understand the basic facts about this operator: its definition, the main theorems about it, and their proofs. This book is an outgrowth of the notes in which I worked this out. For me this was a great learning experience because of the many beautiful mathematical structures which are involved. I thank the Editorial Board of Birkhauser, especially Haim Brezis, for sug gesting the publication of these notes as a book. I am also very grateful for the suggestions by the referees, which have led to substantial improvements in the presentation. Finally I would like to express special thanks to Ann Kostant for her help and her prodding me, in her charming way, into the right direction. J.J. Duistermaat Utrecht, October 16, 1995.
The Heat Kernel Lefschetz Fixed Point Formula For The Spin C Dirac Operator
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Author : J.J. Duistermaat
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-08
The Heat Kernel Lefschetz Fixed Point Formula For The Spin C Dirac Operator written by J.J. Duistermaat 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 2011-07-08 with Mathematics categories.
Reprinted as it originally appeared in the 1990s, this work is as an affordable text that will be of interest to a range of researchers in geometric analysis and mathematical physics. The book covers a variety of concepts fundamental to the study and applications of the spin-c Dirac operator, making use of the heat kernels theory of Berline, Getzlet, and Vergne. True to the precision and clarity for which J.J. Duistermaat was so well known, the exposition is elegant and concise.
Invariance Theory
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Author : Peter B. Gilkey
language : en
Publisher: CRC Press
Release Date : 1994-12-22
Invariance Theory written by Peter B. Gilkey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-22 with Mathematics categories.
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.
Heat Kernels For Elliptic And Sub Elliptic Operators
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Author : Ovidiu Calin
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-10
Heat Kernels For Elliptic And Sub Elliptic Operators written by Ovidiu Calin 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 2010-10-10 with Mathematics categories.
This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes. Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.
The Heat Kernel Lefschetz Fixed Point Formula For The Spin C Dirac Operator
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Author : Johannes Jisse Duistermaat
language : en
Publisher:
Release Date : 1996
The Heat Kernel Lefschetz Fixed Point Formula For The Spin C Dirac Operator written by Johannes Jisse Duistermaat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Almost complex manifolds categories.
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.
Elliptic Boundary Problems For Dirac Operators
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Author : Bernhelm Booss
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-12
Elliptic Boundary Problems For Dirac Operators written by Bernhelm Booss 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 1993-12 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.