Clifford (Geometric) Algebras

1. Front Matter

   Pages i-xvii

   PDF

2. Introduction

   • William E. Baylis

   Pages 1-4

3. Clifford Algebras and Spinor Operators

   • Pertti Lounesto

   Pages 5-35

4. Introduction to Geometric Algebras

   • Garret Sobczyk

   Pages 37-43

5. Linear Transformations

   • Garret Sobczyk

   Pages 45-52

6. Directed Integration

   • Garret Sobczyk

   Pages 53-64

7. Linear Algebra

   • Chris Doran, Anthony Lasenby, Stephen Gull

   Pages 65-82

8. Dynamics

   • Stephen Gull, Chris Doran, Anthony Lasenby

   Pages 83-94

9. Electromagnetism

   • Stephen Gull, Chris Doran, Anthony Lasenby

   Pages 95-110

10. Electron Physics I

    • Stephen Gull, Chris Doran, Anthony Lasenby

    Pages 111-127

11. Electron Physics II

    • Stephen Gull, Chris Doran, Anthony Lasenby

    Pages 129-145

12. STA and the Interpretation of Quantum Mechanics

    • Anthony Lasenby, Stephen Gull, Chris Doran

    Pages 147-169

13. Gravity I — Introduction

    • Anthony Lasenby, Chris Doran, Stephen Gull

    Pages 171-184

14. Gravity II — Field Equations

    • Chris Doran, Anthony Lasenby, Stephen Gull

    Pages 185-195

15. Gravity III — First Applications

    • Anthony Lasenby, Chris Doran, Stephen Gull

    Pages 197-210

16. Gravity IV — The ‘Intrinsic’ Method

    • Chris Doran, Anthony Lasenby, Stephen Gull

    Pages 211-222

17. Gravity V — Further Applications

    • Anthony Lasenby, Chris Doran, Stephen Gull

    Pages 223-235

18. >The Paravector Model of Spacetime

    • William E. Baylis

    Pages 237-252

19. Eigenspinors in Electrodynamics

    • William E. Baylis

    Pages 253-268

20. Eigenspinors in Quantum Theory

    • William E. Baylis

    Pages 269-284

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.

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

"Of interest due to the many provocative physical interpretations of quantum mechanics and gravitational theory suggested by the Clifford algebra approach to these theories."

—Mathematical Reviews

• Department of Physics, University of Windsor, Windsor, Canada

  William E. Baylis

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