The Algebraic Theory of Spinors and Clifford Algebras

The Algebraic Theory of Spinors and Clifford Algebras
Title The Algebraic Theory of Spinors and Clifford Algebras PDF eBook
Author Claude Chevalley
Publisher Springer Science & Business Media
Pages 232
Release 1996-12-13
Genre Mathematics
ISBN 9783540570639

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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.

An Introduction to Clifford Algebras and Spinors

An Introduction to Clifford Algebras and Spinors
Title An Introduction to Clifford Algebras and Spinors PDF eBook
Author Jayme Vaz Jr.
Publisher Oxford University Press
Pages 257
Release 2016
Genre Mathematics
ISBN 0198782926

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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.

The Algebraic Theory of Spinors

The Algebraic Theory of Spinors
Title The Algebraic Theory of Spinors PDF eBook
Author Claude Chevalley
Publisher
Pages 128
Release 1972
Genre Spinor analysis
ISBN

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Clifford Algebras and Spinors

Clifford Algebras and Spinors
Title Clifford Algebras and Spinors PDF eBook
Author Pertti Lounesto
Publisher Cambridge University Press
Pages 352
Release 2001-05-03
Genre Mathematics
ISBN 0521005515

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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.

Clifford Algebra to Geometric Calculus

Clifford Algebra to Geometric Calculus
Title Clifford Algebra to Geometric Calculus PDF eBook
Author David Hestenes
Publisher Springer Science & Business Media
Pages 340
Release 1984
Genre Mathematics
ISBN 9789027725615

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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.

Clifford Algebras and Their Applications in Mathematical Physics

Clifford Algebras and Their Applications in Mathematical Physics
Title Clifford Algebras and Their Applications in Mathematical Physics PDF eBook
Author J.S.R. Chisholm
Publisher Springer Science & Business Media
Pages 589
Release 2012-12-06
Genre Mathematics
ISBN 9400947283

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William Kingdon Clifford published the paper defining his "geometric algebras" in 1878, the year before his death. Clifford algebra is a generalisation to n-dimensional space of quaternions, which Hamilton used to represent scalars and vectors in real three-space: it is also a development of Grassmann's algebra, incorporating in the fundamental relations inner products defined in terms of the metric of the space. It is a strange fact that the Gibbs Heaviside vector techniques came to dominate in scientific and technical literature, while quaternions and Clifford algebras, the true associative algebras of inner-product spaces, were regarded for nearly a century simply as interesting mathematical curiosities. During this period, Pauli, Dirac and Majorana used the algebras which bear their names to describe properties of elementary particles, their spin in particular. It seems likely that none of these eminent mathematical physicists realised that they were using Clifford algebras. A few research workers such as Fueter realised the power of this algebraic scheme, but the subject only began to be appreciated more widely after the publication of Chevalley's book, 'The Algebraic Theory of Spinors' in 1954, and of Marcel Riesz' Maryland Lectures in 1959. Some of the contributors to this volume, Georges Deschamps, Erik Folke Bolinder, Albert Crumeyrolle and David Hestenes were working in this field around that time, and in their turn have persuaded others of the importance of the subject.

Clifford Algebras and their Applications in Mathematical Physics

Clifford Algebras and their Applications in Mathematical Physics
Title Clifford Algebras and their Applications in Mathematical Physics PDF eBook
Author A. Micali
Publisher Springer Science & Business Media
Pages 509
Release 2013-03-09
Genre Mathematics
ISBN 9401580901

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This volume contains selected papers presented at the Second Workshop on Clifford Algebras and their Applications in Mathematical Physics. These papers range from various algebraic and analytic aspects of Clifford algebras to applications in, for example, gauge fields, relativity theory, supersymmetry and supergravity, and condensed phase physics. Included is a biography and list of publications of Mário Schenberg, who, next to Marcel Riesz, has made valuable contributions to these topics. This volume will be of interest to mathematicians working in the fields of algebra, geometry or special functions, to physicists working on quantum mechanics or supersymmetry, and to historians of mathematical physics.