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Author: Jayme Vaz Jr.
Publisher: Oxford University Press
ISBN: 0198782926
Category : Mathematics
Languages : en
Pages : 257
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Book Description
This work is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.
Author: Jayme Vaz Jr.
Publisher: Oxford University Press
ISBN: 0198782926
Category : Mathematics
Languages : en
Pages : 257
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Book Description
This work is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.
Author: Pertti Lounesto
Publisher: Cambridge University Press
ISBN: 0521005515
Category : Mathematics
Languages : en
Pages : 352
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Book Description
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.
Author: Jayme Vaz Jr.
Publisher:
ISBN: 9780191826146
Category : MATHEMATICS
Languages : en
Pages : 242
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Book Description
This book is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.
Author: David Hestenes
Publisher: Springer Science & Business Media
ISBN: 9789027725615
Category : Mathematics
Languages : en
Pages : 340
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Book Description
Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
Author: D. J. H. Garling
Publisher: Cambridge University Press
ISBN: 1107096383
Category : Mathematics
Languages : en
Pages : 209
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Book Description
A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics.
Author: Eckhard Meinrenken
Publisher: Springer Science & Business Media
ISBN: 3642362168
Category : Mathematics
Languages : en
Pages : 331
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Book Description
This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.
Author: Roldao da Rocha, Jr.
Publisher: Oxford University Press, USA
ISBN: 9780198836285
Category : Clifford algebras
Languages : en
Pages : 256
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Book Description
This book provides a unique pedagogical introduction to clifford algebras, with a focus on spinors. It bridges the gap between mathematics and physics, merging both applications and the formal approach. It provides detailed worked examples throughout to help understand the ideas presented.
Author: Élie Cartan
Publisher: Courier Corporation
ISBN: 0486137325
Category : Mathematics
Languages : en
Pages : 193
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Book Description
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: William Eric Baylis
Publisher: Boston : Birkhäuser
ISBN:
Category : Mathematics
Languages : en
Pages : 544
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Book Description
This volume offers a comprehensive approach to the theoretical, applied and symbolic computational aspects of the subject. Excellent for self-study, leading experts in the field have written on the of topics mentioned above, using an easy approach with efficient geometric language for non-specialists.
Author: H. Blaine Lawson
Publisher: Princeton University Press
ISBN: 1400883911
Category : Mathematics
Languages : en
Pages : 442
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Book Description
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.
