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 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 Clifford Algebras and Dirac Operators in Harmonic Analysis written by John E. Gilbert and published by Cambridge University Press. This book was released on 1991-07-26 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dirac Operators in Riemannian Geometry written by Thomas Friedrich and published by American Mathematical Soc.. This book was released on 2000 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 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 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 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 Analysis of Dirac Systems and Computational Algebra written by Fabrizio Colombo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: * The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems * All the necessary classical material is initially presented * Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics
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 Clifford Algebra and Spinor Valued Functions written by R. Delanghe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes the substantial developments in Clifford analysis which have taken place during the last decade and, in particular, the role of the spin group in the study of null solutions of real and complexified Dirac and Laplace operators. The book has six main chapters. The first two (Chapters 0 and I) present classical results on real and complex Clifford algebras and show how lower-dimensional real Clifford algebras are well-suited for describing basic geometric notions in Euclidean space. Chapters II and III illustrate how Clifford analysis extends and refines the computational tools available in complex analysis in the plane or harmonic analysis in space. In Chapter IV the concept of monogenic differential forms is generalized to the case of spin-manifolds. Chapter V deals with analysis on homogeneous spaces, and shows how Clifford analysis may be connected with the Penrose transform. The volume concludes with some Appendices which present basic results relating to the algebraic and analytic structures discussed. These are made accessible for computational purposes by means of computer algebra programmes written in REDUCE and are contained on an accompanying floppy disk.
Download or read book Spectral Analysis of Relativistic Operators written by A. A. Balinsky and published by World Scientific. This book was released on 2011 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the lack of semiboundedness of the Dirac operator, and this has led to the investigation of operators like those of Chandrasekhar-Herbst and Brown-Ravenhall, which are semibounded under appropriate circumstances.This book contains an up-to-date, comprehensive and self-contained analysis of the spectral properties of these operators, providing the tools for anyone working in this area. Another major feature is the work of the authors on zero modes, a topic which has important significance for the stability of matter and other physical problems. Up until now, these topics have been scattered throughout the literature, without a systematic and cohesive treatment. The book will report largely on the progress on these topics published since 1992.
Download or read book Clifford Analysis written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Clifford Algebras in Analysis and Related Topics written by John Ryan and published by CRC Press. This book was released on 1995-10-23 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis. All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains. Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much, much more! Clifford Algebras in Analysis and Related Topics also contains the most comprehensive section on open problems available. The book presents the most detailed link between Clifford analysis and classical harmonic analysis. It is a refreshing break from the many expensive and lengthy volumes currently found on the subject.
Download or read book Handbook of Relativistic Quantum Chemistry written by Wenjian Liu and published by Springer. This book was released on 2016-06-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook covers new methodological developments and applications of relativistic quantum chemistry. It also pays attention to the foundation of relativistic quantum mechanics and addresses a number of fundamental issues that have not been covered by any book. For instance, what is the appropriate relativistic many-electron Hamiltonian? How to do relativistic explicit/local correlation? How to formulate relativistic properties? How to combine double-group and time-reversal symmetries? How to do QED calculations for molecules? Just to name a few. This book aims to establish the big picture of relativistic molecular quantum mechanics, ranging from pedagogic introduction for uninitiated readers, advanced methodologies and efficient algorithms for experts, to possible future perspectives, such that the reader knows when/how to apply/develop the methodologies. This self-contained two-volume book can be regarded as a supplement to the three-volume "Handbook of Computational Chemistry", which contains no relativity at all. It is to be composed of 6 sections with different chapters (will be further expanded), each of which is to be written by the most active experts, who will be invited upon approval of this proposal.
Download or read book Spectral Analysis Of Relativistic Operators written by William Desmond Evans and published by World Scientific. This book was released on 2010-10-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the lack of semiboundedness of the Dirac operator, and this has led to the investigation of operators like those of Chandrasekhar-Herbst and Brown-Ravenhall, which are semibounded under appropriate circumstances.This book contains an up-to-date, comprehensive and self-contained analysis of the spectral properties of these operators, providing the tools for anyone working in this area. Another major feature is the work of the authors on zero modes, a topic which has important significance for the stability of matter and other physical problems. Up until now, these topics have been scattered throughout the literature, without a systematic and cohesive treatment. The book will report largely on the progress on these topics published since 1992./a
Download or read book Dirac Operators and Analysis on Open Manifolds written by Gorm Salomonsen and published by . This book was released on 1996 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt:
