Geometry Spinors And Applications
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Author | : Ian M. Benn |
Publisher | : Institute of Physics Publishing (GB) |
Total Pages | : 376 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : |
"...The aim of this book is to introduce theoretical physicists, of graduate student level upwards, to the methods of differential geometry and Clifford algebras in classical field theory..."--back cover.
Author | : Donal J. Hurley |
Publisher | : Springer |
Total Pages | : 392 |
Release | : 1999-12-16 |
Genre | : Science |
ISBN | : 1852332239 |
This text is a self-contained, comprehensive treatment of the tensor and spinor calculus of space-time manifolds with as few technicalities as correct treatment allows. Both the physical and geometrical motivation of all concepts are discussed, helping the reader to go through the technical details in a confident manner. Several physical theories are discussed and developed beyond standard treatment using results in the book. Both the traditional "index" and modern "coordinate-free" notations are used side-by-side in the book, making it accessible to beginner graduate students in mathematics and physics. The methods developed offer new insights into standard areas of physics, such as classical mechanics or electromagnetism, and takes readers to the frontiers of knowledge of spinor calculus.
Author | : H. Blaine Lawson |
Publisher | : Princeton University Press |
Total Pages | : 442 |
Release | : 2016-06-02 |
Genre | : Mathematics |
ISBN | : 1400883911 |
This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.
Author | : Jayme Vaz Jr. |
Publisher | : Oxford University Press |
Total Pages | : 257 |
Release | : 2016-05-12 |
Genre | : Science |
ISBN | : 0191085782 |
This text explores how Clifford algebras and spinors have been sparking a collaboration and bridging a gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main point of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. Among the existing approaches to Clifford algebras and spinors this book is unique in that it provides a didactical presentation of the topic and is accessible to both students and researchers. It emphasizes the formal character and the deep algebraic and geometric completeness, and merges them with the physical applications. The style is clear and precise, but not pedantic. The sole pre-requisites is a course in Linear Algebra which most students of Physics, Mathematics or Engineering will have covered as part of their undergraduate studies.
Author | : Élie Cartan |
Publisher | : Courier Corporation |
Total Pages | : 193 |
Release | : 2012-04-30 |
Genre | : Mathematics |
ISBN | : 0486137325 |
Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities.
Author | : Claude Chevalley |
Publisher | : Springer Science & Business Media |
Total Pages | : 232 |
Release | : 1996-12-13 |
Genre | : Mathematics |
ISBN | : 9783540570639 |
In 1982, Claude Chevalley expressed three specific wishes with respect to the publication of his Works. First, he stated very clearly that such a publication should include his non technical papers. His reasons for that were two-fold. One reason was his life long commitment to epistemology and to politics, which made him strongly opposed to the view otherwise currently held that mathematics involves only half of a man. As he wrote to G. C. Rota on November 29th, 1982: "An important number of papers published by me are not of a mathematical nature. Some have epistemological features which might explain their presence in an edition of collected papers of a mathematician, but quite a number of them are concerned with theoretical politics ( . . . ) they reflect an aspect of myself the omission of which would, I think, give a wrong idea of my lines of thinking". On the other hand, Chevalley thought that the Collected Works of a mathematician ought to be read not only by other mathematicians, but also by historians of science.
Author | : Christian Perwass |
Publisher | : Springer Science & Business Media |
Total Pages | : 389 |
Release | : 2009-02-11 |
Genre | : Computers |
ISBN | : 3540890688 |
The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and more robust algorithms. This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and applications. The first part includes chapters on random variables in geometric algebra, linear estimation methods that incorporate the uncertainty of algebraic elements, and the representation of geometry in Euclidean, projective, conformal and conic space. The second part is dedicated to applications of geometric algebra, which include uncertain geometry and transformations, a generalized camera model, and pose estimation. Graduate students, scientists, researchers and practitioners will benefit from this book. The examples given in the text are mostly recent research results, so practitioners can see how to apply geometric algebra to real tasks, while researchers note starting points for future investigations. Students will profit from the detailed introduction to geometric algebra, while the text is supported by the author's visualization software, CLUCalc, freely available online, and a website that includes downloadable exercises, slides and tutorials.
Author | : Philip Charlton |
Publisher | : |
Total Pages | : 240 |
Release | : 1997 |
Genre | : Clifford algebras |
ISBN | : |
Author | : Roger Penrose |
Publisher | : Cambridge University Press |
Total Pages | : 516 |
Release | : 1984 |
Genre | : Mathematics |
ISBN | : 9780521347860 |
In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields.
Author | : Pertti Lounesto |
Publisher | : Cambridge University Press |
Total Pages | : 352 |
Release | : 2001-05-03 |
Genre | : Mathematics |
ISBN | : 0521005515 |
This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras.