© D. Hestenes (1998)
Preface This is a book in progress, so it will be modified as expanded
as time allows. It is a concise update of the book Space-Time Algebra (STA).
The basic algebraic structure of STA remains the same, having passed the test of time.
The treatment of electrodynamics has also survived but has expanded. The
main changes are in quantum theory and gravitation, where substantial advances
have been made, some quite recently.
Introduction
PART I: Mathematical Fundamentals
1. Spacetime Algebra
2. Vector Derivatives and Differentials
3. Linear Algebra
4. Spacetime Splits
5. Rigid Bodies and Charged Particles
6. Electromagnetic Fields
7. Transformations on Spacetime
8. Directed Integrals and the Fundamental Theorem
9. Integral Equations and Conservation Laws
PART II: Quantum Theory
10. The Real Dirac Equation
11. Observables and Conservation Laws
12. Electron Trajectories
13. The Zitterbewegung Interpretation
14. Electroweak Interactions
Part III. Induced Geometry on Flat Spacetime
15. Gauge Tensor and Gauge Invariance
16. Covariant Derivatives and Curvature
17. Universal Laws for Spacetime Physics
References
Appendix A. Tensors and their Classification
Appendix B: Transformations and Invariants
Appendix C: Lagrangian Formulation
Related Papers
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