Tensors And The Clifford Algebra

Author : Alphonse Charlier,Alain Berard,Marie-France Charlier,Daniele Fristot
Publisher : CRC Press
Page : 352 pages
File Size : 54,6 Mb
Release : 1992-06-16
Category : Mathematics
ISBN : 0824786661

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Tensors and the Clifford Algebra by Alphonse Charlier,Alain Berard,Marie-France Charlier,Daniele Fristot Pdf

This practical reference and text presents the applications of tensors, Lie groups and algebra to Maxwell, Klein-Gordon and Dirac equations, making elementary theoretical physics comprehensible and high-level theoretical physics accessible.;Providing the fundamental mathematics necessary to understand the applications, Tensors and the Clifford Algebra offers lucid discussions of covariant tensor calculus; examines subjects from a variety of perspectives; supplies highly detailed developments of all calculations; employs the language of physics in its explanations; and illustrates the use of Clifford algebra and tensor calculus in studying bosons and fermions.;With over 2800 display equations and 14 appendixes, this book should be a useful reference for mathematical physicists and applied mathematicians, and an important text for upper-level undergraduate and graduate students in quantum mechanics, relativity, electromagnetism, theoretical physics, elasticity and field theory courses.

Author : Alphonse Charlier,Alain Berard,Marie-France Charlier,Daniele Fristot
Publisher : CRC Press
Page : 352 pages
File Size : 55,8 Mb
Release : 2020-08-26
Category : Mathematics
ISBN : 9781000147995

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Tensors and the Clifford Algebra by Alphonse Charlier,Alain Berard,Marie-France Charlier,Daniele Fristot Pdf

This practical reference and text presents the applications of tensors, Lie groups and algebra to Maxwell, Klein-Gordon and Dirac equations, making elementary theoretical physics comprehensible and high-level theoretical physics accessible.;Providing the fundamental mathematics necessary to understand the applications, Tensors and the Clifford Algebra offers lucid discussions of covariant tensor calculus; examines subjects from a variety of perspectives; supplies highly detailed developments of all calculations; employs the language of physics in its explanations; and illustrates the use of Clifford algebra and tensor calculus in studying bosons and fermions.;With over 2800 display equations and 14 appendixes, this book should be a useful reference for mathematical physicists and applied mathematicians, and an important text for upper-level undergraduate and graduate students in quantum mechanics, relativity, electromagnetism, theoretical physics, elasticity and field theory courses.

Author : Rafal Ablamowicz
Publisher : Springer Science & Business Media
Page : 635 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220442

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Clifford Algebras by Rafal Ablamowicz Pdf

The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.

Author : Jayme Vaz Jr.,Roldão da Rocha Jr.
Publisher : Oxford University Press
Page : 257 pages
File Size : 43,5 Mb
Release : 2016
Category : Mathematics
ISBN : 9780198782926

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An Introduction to Clifford Algebras and Spinors by Jayme Vaz Jr.,Roldão da Rocha Jr. Pdf

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 : Robert Hermann
Publisher : Math-Sci Press
Page : 292 pages
File Size : 50,5 Mb
Release : 1974
Category : Mathematics
ISBN : 0915692066

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Spinors, Clifford and Cayley Algebras by Robert Hermann Pdf

Author : Alan Macdonald
Publisher : Createspace Independent Publishing Platform
Page : 0 pages
File Size : 54,9 Mb
Release : 2012
Category : Calculus
ISBN : 1480132454

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Vector and Geometric Calculus by Alan Macdonald Pdf

This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. This is the printing of August 2022. The book is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one. Its web page is at faculty.luther.edu/ macdonal/laga. Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways. Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world. Differential geometry is used today in many disciplines. A final chapter is devoted to it. Download the book's table of contents, preface, and index at the book's web site: faculty.luther.edu/ macdonal/vagc. From a review of Linear and Geometric Algebra: Alan Macdonald's text is an excellent resource if you are just beginning the study of geometric algebra and would like to learn or review traditional linear algebra in the process. The clarity and evenness of the writing, as well as the originality of presentation that is evident throughout this text, suggest that the author has been successful as a mathematics teacher in the undergraduate classroom. This carefully crafted text is ideal for anyone learning geometric algebra in relative isolation, which I suspect will be the case for many readers. -- Jeffrey Dunham, William R. Kenan Jr. Professor of Natural Sciences, Middlebury College

Author : George Frederick James Temple
Publisher : Courier Corporation
Page : 114 pages
File Size : 51,7 Mb
Release : 2004-09-01
Category : Mathematics
ISBN : 0486439089

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Cartesian Tensors by George Frederick James Temple Pdf

An introduction to the theory of Cartesian tensors, this text notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. Covers isotropic tensors and spinor analysis within the confines of Euclidean space; and tensors in orthogonal curvilinear coordinates. Examples. 1960 edition.

Author : Pertti Lounesto
Publisher : Cambridge University Press
Page : 352 pages
File Size : 42,5 Mb
Release : 2001-05-03
Category : Mathematics
ISBN : 9780521005517

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Clifford Algebras and Spinors by Pertti Lounesto Pdf

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 : A. Micali,R. Boudet,J. Helmstetter
Publisher : Springer Science & Business Media
Page : 509 pages
File Size : 46,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401580908

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Clifford Algebras and their Applications in Mathematical Physics by A. Micali,R. Boudet,J. Helmstetter Pdf

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.

Author : D. Hestenes,Garret Sobczyk
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400962927

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Clifford Algebra to Geometric Calculus by D. Hestenes,Garret Sobczyk Pdf

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 Algebm' 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 quatemions, 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 : David Hestenes,Garret Sobczyk
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 45,5 Mb
Release : 1984
Category : Mathematics
ISBN : 9027725616

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Clifford Algebra to Geometric Calculus by David Hestenes,Garret Sobczyk Pdf

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 : Adam Marsh
Publisher : World Scientific
Page : 301 pages
File Size : 45,8 Mb
Release : 2017-11-27
Category : Science
ISBN : 9789813233935

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Mathematics For Physics: An Illustrated Handbook by Adam Marsh Pdf

This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but compact, and the emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints. Certain topics which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations, are avoided. The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.

Author : Rafal Ablamowicz,P. Lounesto
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 50,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401584227

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Clifford Algebras and Spinor Structures by Rafal Ablamowicz,P. Lounesto Pdf

This volume is dedicated to the memory of Albert Crumeyrolle, who died on June 17, 1992. In organizing the volume we gave priority to: articles summarizing Crumeyrolle's own work in differential geometry, general relativity and spinors, articles which give the reader an idea of the depth and breadth of Crumeyrolle's research interests and influence in the field, articles of high scientific quality which would be of general interest. In each of the areas to which Crumeyrolle made significant contribution - Clifford and exterior algebras, Weyl and pure spinors, spin structures on manifolds, principle of triality, conformal geometry - there has been substantial progress. Our hope is that the volume conveys the originality of Crumeyrolle's own work, the continuing vitality of the field he influenced, and the enduring respect for, and tribute to, him and his accomplishments in the mathematical community. It isour pleasure to thank Peter Morgan, Artibano Micali, Joseph Grifone, Marie Crumeyrolle and Kluwer Academic Publishers for their help in preparingthis volume.

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 54,9 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780821869079

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Tensors: Geometry and Applications by J. M. Landsberg Pdf

Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

Author : F. Brackx,R. Delanghe,H. Serras
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401120067

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Clifford Algebras and their Applications in Mathematical Physics by F. Brackx,R. Delanghe,H. Serras Pdf

This International Conference on Clifford AlgebrfU and Their Application, in Math ematical Phy,ic, is the third in a series of conferences on this theme, which started at the Univer,ity of Kent in Canterbury in 1985 and was continued at the Univer,iU de, Science, et Technique, du Languedoc in Montpellier in 1989. Since the start of this series of Conferences the research fields under consideration have evolved quite a lot. The number of scientific papers on Clifford Algebra, Clifford Analysis and their impact on the modelling of physics phenomena have increased tremendously and several new books on these topics were published. We were very pleased to see old friends back and to wellcome new guests who by their inspiring talks contributed fundamentally to tracing new paths for the future development of this research area. The Conference was organized in Deinze, a small rural town in the vicinity of the University town Gent. It was hosted by De Ceder, a vacation and seminar center in a green area, a typical landscape of Flanders's "plat pays" . The Conference was attended by 61 participants coming from 18 countries; there were 10 main talks on invitation, 37 contributions accepted by the Organizing Com mittee and a poster session. There was also a book display of Kluwer Academic Publishers. As in the Proceedings of the Canterbury and Montpellier conferences we have grouped the papers accordingly to the themes they are related to: Clifford Algebra, Clifford Analysis, Classical Mechanics, Mathematical Physics and Physics Models.