Heat Kernels And Dirac Operators

Author : Nicole Berline,Ezra Getzler,Michèle Vergne
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 40,6 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 3540200622

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Heat Kernels and Dirac Operators by Nicole Berline,Ezra Getzler,Michèle Vergne Pdf

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 : J.J. Duistermaat
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 47,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461253440

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The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator by J.J. Duistermaat Pdf

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.

Author : Johannes Jisse Duistermaat
Publisher : Unknown
Page : 247 pages
File Size : 50,8 Mb
Release : 1996
Category : Almost complex manifolds
ISBN : 3764338652

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The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator by Johannes Jisse Duistermaat Pdf

Author : Anonim
Publisher : Unknown
Page : 260 pages
File Size : 47,5 Mb
Release : 2011-12-03
Category : Electronic
ISBN : 0817682481

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The Heat Kernel Lefschetz Fixed Point Formula for the Spin-C Dirac Operator by Anonim Pdf

Author : Ovidiu Calin,Der-Chen Chang,Kenro Furutani,Chisato Iwasaki
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 49,8 Mb
Release : 2010-10-10
Category : Mathematics
ISBN : 9780817649951

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Heat Kernels for Elliptic and Sub-elliptic Operators by Ovidiu Calin,Der-Chen Chang,Kenro Furutani,Chisato Iwasaki Pdf

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.

Author : Giampiero Esposito
Publisher : Cambridge University Press
Page : 227 pages
File Size : 40,7 Mb
Release : 1998-08-20
Category : Mathematics
ISBN : 9780521648622

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Dirac Operators and Spectral Geometry by Giampiero Esposito Pdf

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 : Bernhelm Booß-Bavnbek,Krzysztof P. Wojciechhowski
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203377

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Elliptic Boundary Problems for Dirac Operators by Bernhelm Booß-Bavnbek,Krzysztof P. Wojciechhowski Pdf

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.

Author : Alexander Grigoryan
Publisher : American Mathematical Soc.
Page : 504 pages
File Size : 52,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821849354

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Heat Kernel and Analysis on Manifolds by Alexander Grigoryan Pdf

"This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and p -Laplace operators, heat kernel and spherical inversion on SL 2 (C) , random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs."--Publisher's website.

Author : Jay Jorgenson,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 51,8 Mb
Release : 2006
Category : Geometry, Algebraic
ISBN : 9780821836989

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The Ubiquitous Heat Kernel by Jay Jorgenson,American Mathematical Society Pdf

The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.

Author : Ivan Avramidi
Publisher : Birkhäuser
Page : 390 pages
File Size : 52,5 Mb
Release : 2015-11-26
Category : Mathematics
ISBN : 9783319262666

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Heat Kernel Method and its Applications by Ivan Avramidi Pdf

The heart of the book is the development of a short-time asymptotic expansion for the heat kernel. This is explained in detail and explicit examples of some advanced calculations are given. In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented. The book consists of four parts: Analysis, Geometry, Perturbations and Applications. The first part shortly reviews of some background material and gives an introduction to PDEs. The second part is devoted to a short introduction to various aspects of differential geometry that will be needed later. The third part and heart of the book presents a systematic development of effective methods for various approximation schemes for parabolic differential equations. The last part is devoted to applications in financial mathematics, in particular, stochastic differential equations. Although this book is intended for advanced undergraduate or beginning graduate students in, it should also provide a useful reference for professional physicists, applied mathematicians as well as quantitative analysts with an interest in PDEs.

Author : John E. Gilbert,Margaret Anne Marie Murray
Publisher : Cambridge University Press
Page : 346 pages
File Size : 51,5 Mb
Release : 1991-07-26
Category : Mathematics
ISBN : 0521346541

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Clifford Algebras and Dirac Operators in Harmonic Analysis by John E. Gilbert,Margaret Anne Marie Murray Pdf

The aim of this book is to unite the seemingly disparate topics of Clifford algebras, analysis on manifolds, and harmonic analysis. The authors show how algebra, geometry, and differential equations play a more fundamental role in Euclidean Fourier analysis. They then link their presentation of the Euclidean theory naturally to the representation theory of semi-simple Lie groups.

Author : Richard Melrose
Publisher : CRC Press
Page : 392 pages
File Size : 46,9 Mb
Release : 1993-03-31
Category : Mathematics
ISBN : 9781439864609

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The Atiyah-Patodi-Singer Index Theorem by Richard Melrose Pdf

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
Page : 534 pages
File Size : 46,6 Mb
Release : 1994-12-22
Category : Mathematics
ISBN : 0849378745

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Invariance Theory by Peter B. Gilkey Pdf

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.

Author : Bernhelm Booss,Krzysztof P. Wojciechowski
Publisher : World Scientific
Page : 553 pages
File Size : 51,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812773609

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Analysis, Geometry and Topology of Elliptic Operators by Bernhelm Booss,Krzysztof P. Wojciechowski Pdf

Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski''s work in the theory of elliptic operators. Sample Chapter(s). Contents (42 KB). Contents: On the Mathematical Work of Krzysztof P Wojciechowski: Selected Aspects of the Mathematical Work of Krzysztof P Wojciechowski (M Lesch); Gluing Formulae of Spectral Invariants and Cauchy Data Spaces (J Park); Topological Theories: The Behavior of the Analytic Index under Nontrivial Embedding (D Bleecker); Critical Points of Polynomials in Three Complex Variables (L I Nicolaescu); Chern-Weil Forms Associated with Superconnections (S Paycha & S Scott); Heat Kernel Calculations and Surgery: Non-Laplace Type Operators on Manifolds with Boundary (I G Avramidi); Eta Invariants for Manifold with Boundary (X Dai); Heat Kernels of the Sub-Laplacian and the Laplacian on Nilpotent Lie Groups (K Furutani); Remarks on Nonlocal Trace Expansion Coefficients (G Grubb); An Anomaly Formula for L 2- Analytic Torsions on Manifolds with Boundary (X Ma & W Zhang); Conformal Anomalies via Canonical Traces (S Paycha & S Rosenberg); Noncommutative Geometry: An Analytic Approach to Spectral Flow in von Neumann Algebras (M-T Benameur et al.); Elliptic Operators on Infinite Graphs (J Dodziuk); A New Kind of Index Theorem (R G Douglas); A Note on Noncommutative Holomorphic and Harmonic Functions on the Unit Disk (S Klimek); Star Products and Central Extensions (J Mickelsson); An Elementary Proof of the Homotopy Equivalence between the Restricted General Linear Group and the Space of Fredholm Operators (T Wurzbacher); Theoretical Particle, String and Membrane Physics, and Hamiltonian Dynamics: T-Duality for Non-Free Circle Actions (U Bunke & T Schick); A New Spectral Cancellation in Quantum Gravity (G Esposito et al.); A Generalized Morse Index Theorem (C Zhu). Readership: Researchers in modern global analysis and particle physics.

Author : Matthias Lesch,Weiping Zhang,Slawomir Klimek,Bernhelm Booss-bavnbek
Publisher : World Scientific
Page : 553 pages
File Size : 53,8 Mb
Release : 2006-04-25
Category : Mathematics
ISBN : 9789814478021

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Analysis, Geometry And Topology Of Elliptic Operators: Papers In Honor Of Krzysztof P Wojciechowski by Matthias Lesch,Weiping Zhang,Slawomir Klimek,Bernhelm Booss-bavnbek Pdf

Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics.The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski's work in the theory of elliptic operators.