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Clifford Algebras and Their Applications in Mathematical Physics

  • J. S. R. Chisholm
  • A. K. Common

Part of the NATO ASI Series book series (ASIC, volume 183)

Table of contents

  1. Front Matter
    Pages i-xix
  2. General Surveys

    1. Pertti Lounesto
      Pages 25-37
  3. Classification of Clifford Algebras

  4. Spin Groups

  5. Clifford Analysis

  6. Mathematical Physics

  7. Physical Models

  8. Electromagnetism

  9. Generalisations of Clifford Algebra

    1. A. Crumeyrolle
      Pages 517-529
    2. Per-Erik Hagmark, Pertti Lounesto
      Pages 531-540
    3. Jacques Helmstetter
      Pages 559-564

About this book

Introduction

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.

Keywords

algebra calculus differential equation gauge theory mathematical physics minimum

Editors and affiliations

  • J. S. R. Chisholm
    • 1
  • A. K. Common
    • 1
  1. 1.Mathematical InstituteUniversity of KentCanterbury, KentUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-4728-3
  • Copyright Information Springer Science+Business Media B.V. 1986
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-8602-8
  • Online ISBN 978-94-009-4728-3
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site
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