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Lectures on Clifford (Geometric) Algebras and Applications
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.
Conformal Groups in Geometry and Spin Structures
This book provides a self-contained overview of the role of conformal groups in geometry and mathematical physics. It features a careful development of the material, from the basics of Clifford algebras to more advanced topics. Each chapter covers a specific aspect of conformal groups and conformal spin geometry. All major concepts are introduced and followed by detailed descriptions and definitions, and a comprehensive bibliography and index round out the work. Rich in exercises that are accompanied by full proofs and many hints, the book will be ideal as a course text or self-study volume for senior undergraduates and graduate students.
Geometric Algebra with Applications in Science and Engineering
The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hesten...
Clifford Algebras in Analysis and Related Topics
This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis. All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integral...
Clifford Numbers and Spinors
Marcellliesz's lectures delivered on October 1957 -January 1958 at the Uni versity of Maryland, College Park, have been previously published only infor mally as a manuscript entitled CLIFFORD NUMBERS AND SPINORS (Chap ters I - IV). As the title says, the lecture notes consist of four Chapters I, II, III and IV. However, in the preface of the lecture notes lliesz refers to Chapters V and VI which he could not finish. Chapter VI is mentioned on pages 1, 3, 16, 38 and 156, which makes it plausible that lliesz was well aware of what he was going to include in the final missing chapters. The present book makes lliesz's classic lecture notes generally available to a wider audience and tries somewhat to fill in one of the last missing chapters. This book also tries to evaluate lliesz's influence on the present research on Clifford algebras and draws special attention to lliesz's contributions in this field - often misunderstood.
