Download or read book Introduction to Symplectic Dirac Operators written by Katharina Habermann and published by Springer. This book was released on 2006-10-28 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.
Download or read book An Introduction to Dirac Operators on Manifolds written by Jan Cnops and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 219 pages. 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
Download or read book The Index Formula for Dirac Operators written by Levi Lopes de Lima and published by . This book was released on 2003 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Mp c structures and Symplectic Dirac Operators written by Michel Cahen and published by . This book was released on 2013 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dirac Operators and Spectral Geometry written by Giampiero Esposito and published by Cambridge University Press. This book was released on 1998-08-20 with total page 227 pages. 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.
Download or read book The Dirac Spectrum written by Nicolas Ginoux and published by Springer Science & Business Media. This book was released on 2009-06-11 with total page 168 pages. 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.
Download or read book Heat Kernels and Dirac Operators written by Nicole Berline and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 384 pages. 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.
Download or read book Dirac Operators in Representation Theory written by Jing-Song Huang and published by Springer Science & Business Media. This book was released on 2007-05-27 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Heat Kernel Lefschetz Fixed Point Formula for the Spin c Dirac Operator written by J.J. Duistermaat and published by Springer Science & Business Media. This book was released on 2011-07-08 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Symplectic Dirac Operators on K hler Manifolds written by Katharina Habermann and published by . This book was released on 1997 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dirac Operators in Analysis written by John Ryan and published by CRC Press. This book was released on 1999-01-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clifford analysis has blossomed into an increasingly relevant and fashionable area of research in mathematical analysis-it fits conveniently at the crossroads of many fundamental areas of research, including classical harmonic analysis, operator theory, and boundary behavior. This book presents a state-of-the-art account of the most recent developments in the field of Clifford analysis with contributions by many of the field's leading researchers.
Download or read book Elliptic Boundary Problems for Dirac Operators written by Bernhelm Booß-Bavnbek and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Symplectic Dirac Operators and a Splitting Property for the Symplectic Spinor Bundle written by Katharina Habermann and published by . This book was released on 1999 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd Dimensional Manifold with Boundary written by Paul Kirk and published by American Mathematical Soc.. This book was released on 1996 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analytic perturbation theory for eigenvalues of Dirac operators on odd dimensional manifolds with boundary is described in terms of [italic]extended L2 eigenvectors [end italics] on manifolds with cylindrical ends. These are generalizations of the Atiyah-Patodi-Singer extended [italic capital]L2 kernel of a Dirac operator. We prove that they form a discrete set near zero and deform analytically, in contrast to [italic capital]L2 eigenvectors, which can be absorbed into the continuous spectrum under deformations when the tangential operator is not invertible. We show that the analytic deformation theory for extended [italic capital]L2 eigenvectors and Atiyah-Patodi-Singer eigenvectors coincides.
Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Download or read book Clifford Analysis and Its Applications written by F. Brackx and published by Springer Science & Business Media. This book was released on 2001-07-31 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation. From the beginning, however, the theory was used and applied to problems in other fields of mathematics, numerical analysis, and mathematical physics. recently, the theory has enlarged its scope considerably by incorporating geometrical methods from global analysis on manifolds and methods from representation theory. New, interesting branches of the theory are based on conformally invariant, first-order systems other than the Dirac equation, or systems that are invariant with respect to a group other than the conformal group. This book represents an up-to-date review of Clifford analysis in its present form, its applications, and directions for future research. Readership: Mathematicians and theoretical physicists interested in Clifford analysis itself, or in its applications to other fields.
Download or read book Geometric Properties of Banach Spaces and Nonlinear Iterations written by Charles Chidume and published by Springer Science & Business Media. This book was released on 2009-03-27 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.
