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Clifford (Geometric) Algebras

With Applications to Physics, Mathematics, and Engineering

  • William E. Baylis

Table of contents

  1. Front Matter
    Pages i-xvii
  2. William E. Baylis
    Pages 1-4
  3. Pertti Lounesto
    Pages 5-35
  4. Garret Sobczyk
    Pages 37-43
  5. Garret Sobczyk
    Pages 45-52
  6. Garret Sobczyk
    Pages 53-64
  7. Chris Doran, Anthony Lasenby, Stephen Gull
    Pages 65-82
  8. Stephen Gull, Chris Doran, Anthony Lasenby
    Pages 83-94
  9. Stephen Gull, Chris Doran, Anthony Lasenby
    Pages 95-110
  10. Stephen Gull, Chris Doran, Anthony Lasenby
    Pages 111-127
  11. Stephen Gull, Chris Doran, Anthony Lasenby
    Pages 129-145
  12. Anthony Lasenby, Stephen Gull, Chris Doran
    Pages 147-169
  13. Anthony Lasenby, Chris Doran, Stephen Gull
    Pages 171-184
  14. Chris Doran, Anthony Lasenby, Stephen Gull
    Pages 185-195
  15. Anthony Lasenby, Chris Doran, Stephen Gull
    Pages 197-210
  16. Chris Doran, Anthony Lasenby, Stephen Gull
    Pages 211-222
  17. Anthony Lasenby, Chris Doran, Stephen Gull
    Pages 223-235
  18. William E. Baylis
    Pages 237-252
  19. William E. Baylis
    Pages 253-268
  20. William E. Baylis
    Pages 269-284
  21. William E. Baylis
    Pages 285-296
  22. James P. Crawford
    Pages 297-306
  23. James P. Crawford
    Pages 307-316
  24. James P. Crawford
    Pages 317-327
  25. James P. Crawford
    Pages 329-340
  26. James P. Crawford
    Pages 341-351
  27. James P. Crawford
    Pages 353-364
  28. J. S. R. Chisholm, R. S. Farwell
    Pages 365-388
  29. Bernard Jancewicz
    Pages 389-421
  30. Johannes G. Maks
    Pages 449-457
  31. Collin C. Carbno
    Pages 459-462
  32. Rafal Ablamowicz
    Pages 463-501
  33. Back Matter
    Pages 503-517

About these proceedings

Introduction

This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP), held in Banff, Alberta, in the Canadian Rockies, from July 30 to August 12,1995. The chapters, based on lectures given at the School, are designed to be tutorial in nature, and many include exercises to assist the learning process. Most lecturers gave three or four fifty-minute lectures aimed at relative novices in the field. More emphasis is therefore placed on pedagogy and establishing comprehension than on erudition and superior scholarship. Of course, new and exciting results are presented in applications of Clifford algebras, but in a coherent and user-friendly way to the nonspecialist. The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach, many concepts in physics are clarified, united, and extended in new and sometimes surprising directions. In particular, the approach eliminates the formal gaps that traditionally separate clas­ sical, quantum, and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating, and it suggests resolutions to a major physics problem of the twentieth century, namely how to unite quantum theory and gravity. The term "geometric algebra" was used by Clifford himself, and David Hestenes has suggested its use in order to emphasize its wide applicability, and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann, Hamilton, Rodrigues, Gauss, and others.

Keywords

Albert Einstein Physics Potential Riemannian geometry Theoretical physics algebra covariant derivative curvature electrodynamics electromagnetic wave homomorphism manifold scattering theory

Editors and affiliations

  • William E. Baylis
    • 1
  1. 1.Department of PhysicsUniversity of WindsorWindsorCanada

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