SpaceTime Calculus
© 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.
Table of Contents
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
- Abstract: Spacetime algebra is employed to formulate classical relativistic
mechanics without coordinates. Observers are treated on the same
footing as other physical systems. The kinematics of a rigid body are
expressed in spinor form and the Thomas precession is derived.
- D. Hestenes, J. Math. Phys. 15, 1768-1777 (1974).
© American Institute of Physics.
- Abstract: A spinor formulation of the classical Lorentz force is given which describes the presession
of an electron's spin as well as its velocity. Solutions are worked out applicable to an electron in a
uniform field, plane wave, and a Coulomb field.
- D. Hestenes, J. Math. Phys. 15, 1778-1786 (1974).
© American Institute of Physics.
- Abstract: Geometric Algebra makes it possible to formulate simple spinor equations of motion
for classical particles and rigid bodies. In the Newtonian case, these equations have proven their
value by simplifying orbital computations. The relativistic case is not so well known, but it has
new and surprising features worth exploiting, including close connections to quantum mechanical
equations. The current status of spinor particle mechanics is reviewed, and directions for extention
are pointed out.
- D. Hestenes, Proceedings of the Fourth International Conference on Clifford Algebras
and Their Applications to Mathematical Physics, Aachen/Germany (May 1996).
© Kluwer Academic Publishers, Dordrecht..