Space-Time Algebra

David Hestenes

© Gordon & Breach (1966).


Contents

Introduction

Part I: Geometric Algebra
1. Intrepretation of Clifford Algebra
2. Definition of Clifford Algebra
3. Inner and Outer Products
4. Structure of Clifford Algebra
5. Reversion, Scalar Product
6. The Algebra of Space
7. The Algebra of Space-Time

Part II: Electrodynamics
8. Maxwell's Equation
9. Stress-Energy Vectors
10. Invariants
11. Free Fields

Part III: Dirac Fields
12. Spinors
13. Dirac's Equation
14. Conserved Currents
15. C, P, T

Part IV: Lorentz Transformations
16. Reflections and Rotations
17. Coordinate Transformations
18. Timelike Rotations
19. Scalar Product

Part V: Geometric Calculus
20. Differentiation
21. Coordinate Transformations
22. Integration
23. Global and Local Relativity
24. Gauge Transformation and Spinor Derivatives

Conclusion

Appendices
A. Bases and Pseudoscalars
B. Some Theorems
C. Composition of Spacial Rotations
D. Matrix Representation of the Pauli Algebra

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