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Lectures on Clifford (Geometric) Algebras and Applications
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From the reviews: "...This book is recommended reading for beginning graduate students and other newcomers in this field. The authors of each chapter are world leading experts in their fields and the chapters are well written and organized. In spite of the introductory level of each chapter, many references are given which will help the interested reader go deeper into the subject of interest. Moreover, an appendix written by the editors gives a summary of the existing Clifford algebra software for symbolic computations."—Mathematical Reviews "This text contains a set of lectures presented by P. Lounesto, Introduction to Clifford Algebras; I. Porteous, Mathematical Structure of Clifford Algebras; J. Ryan, Clifford Analysis; W.E. Baylis, Applications of Clifford Algebras in Physics; J.M. Selig, Clifford Algebras in Engineering; T. Branson, Clifford Bundles and Clifford Algebras; and an appendix by R. Ablamowicz and G. Sobczyk describing software for solving different kinds of problems involving computations with Clifford algebras. Each one of the lectures is a jewel and will be appreciated [by] newcomers wanting an introduction to a rapidly developing field as well [as] by practitioners, [who] for pleasure certainly will enjoy reading the texts of those well-known experts...."—Zentralblatt Math "The book under review contains the series of lectures on Clifford Geometric Algebras … . the principal aim of the book to provide beginning graduate students in mathematics and physics and other who are new-interested with no prior knowledge in the secrets of Clifford algebras has been achieved. … the presented material subsumes research activities and some of the recent scientific advances of this theory, and it is an useful learning tool for scientists and engineers from academia and industry." (Clementina D. Mladenova, Journal of Geometry and Symmetry in Physics, Issue 3, 2005)
Kurzbeschreibung
The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird's-eye view of the discipline is presented by six of the world's leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics, physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications.
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ABSTRACT Clifford algebras of lower-dimensional Euclidean spaces and Min-kowski spacetime are discussed and identified with their matrix images. Lesen Sie die erste Seite
Buchdeckel | Copyright | Inhaltsverzeichnis | Auszug | Stichwortverzeichnis | Rückseite
ABSTRACT Clifford algebras of lower-dimensional Euclidean spaces and Min-kowski spacetime are discussed and identified with their matrix images. Lesen Sie die erste Seite
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Buchdeckel | Copyright | Inhaltsverzeichnis | Auszug | Stichwortverzeichnis | Rückseite
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From Clifford Algebra to Geometric Algebra
21. August 2004
Format:Taschenbuch
This is a very interesting little book on Clifford algebras and applications. It contains six lectures. The editors have written an appendix where a brief review of existing software for computations with Clifford algebras is also presented.
The first lecture, by the late Professor Pertti Lounesto, is a concise but very clear and pedagogically brilliant introduction to Clifford algebras. A more extensive overview can be found in his book "Clifford Algebras and Spinors" (Cambridge University Press, Cambridge, 2nd ed., 2001).
The second lecture, by Ian Porteous, analyzes the mathematical structure of Clifford algebras for real and complex nondegenerate quadratic spaces of arbitrary rank and signature. The third lecture, by John Ryan, focuses on Clifford analysis. The fifth lecture, by J. M. Selig, explores some applications of Clifford algebras in engineering. Finally, in the sixth (and last) lecture, Thomas Branson explains some applications of Clifford algebras in differential geometry.
However, from my perspective, the fourth lecture by William E. Baylis is the most controversial. In fact, the application of Clifford algebras in physics is too important. The discussion on the merits of the so-called algebra of physical space (APS) over the spacetime algebra (STA) of David Hestenes is biased: the author advocates the use of APS as in his book "Electrodynamics: A Modern Geometric Approach" (Birkhäuser, Boston, 1999).
Hestenes' STA is the most clear and efficient framework to deal with relativity: actually, it is the fact that STA can easily display the invariants that makes its superiority as a real Geometric Algebra - not only another Clifford Algebra. Besides, the complex paravectors of APS transform the neat structure of Clifford Algebra into a real mess: the geometric interpretation of complex numbers is based on C as a real algebra - not as a field.
The first lecture, by the late Professor Pertti Lounesto, is a concise but very clear and pedagogically brilliant introduction to Clifford algebras. A more extensive overview can be found in his book "Clifford Algebras and Spinors" (Cambridge University Press, Cambridge, 2nd ed., 2001).
The second lecture, by Ian Porteous, analyzes the mathematical structure of Clifford algebras for real and complex nondegenerate quadratic spaces of arbitrary rank and signature. The third lecture, by John Ryan, focuses on Clifford analysis. The fifth lecture, by J. M. Selig, explores some applications of Clifford algebras in engineering. Finally, in the sixth (and last) lecture, Thomas Branson explains some applications of Clifford algebras in differential geometry.
However, from my perspective, the fourth lecture by William E. Baylis is the most controversial. In fact, the application of Clifford algebras in physics is too important. The discussion on the merits of the so-called algebra of physical space (APS) over the spacetime algebra (STA) of David Hestenes is biased: the author advocates the use of APS as in his book "Electrodynamics: A Modern Geometric Approach" (Birkhäuser, Boston, 1999).
Hestenes' STA is the most clear and efficient framework to deal with relativity: actually, it is the fact that STA can easily display the invariants that makes its superiority as a real Geometric Algebra - not only another Clifford Algebra. Besides, the complex paravectors of APS transform the neat structure of Clifford Algebra into a real mess: the geometric interpretation of complex numbers is based on C as a real algebra - not as a field.
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