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Book Categories |
Preface | ||
Acknowledgments | ||
Introduction | 1 | |
Ch. 1 | Geometrical Structure of M | 7 |
1.1 | Preliminaries | 7 |
1.2 | Minkowski Spacetime | 9 |
1.3 | The Lorentz Group | 15 |
1.4 | Timelike Vectors and Curves | 46 |
1.5 | Spacelike Vectors | 61 |
1.6 | Causality Relations | 64 |
1.7 | Spin Transformations and the Lorentz Group | 74 |
1.8 | Particles and Interactions | 87 |
Ch. 2 | Skew-Symmetric Linear Transformations and Electromagnetic Fields | 100 |
2.1 | Motivation via the Lorentz Law | 100 |
2.2 | Elementary Properties | 101 |
2.3 | Invariant Subspaces | 107 |
2.4 | Canonical Forms | 113 |
2.5 | The Energy-Momentum Transformation | 117 |
2.6 | Motion in Constant Fields | 121 |
2.7 | Variable Electromagnetic Fields | 126 |
Ch. 3 | The Theory of Spinors | 143 |
3.1 | Representations of the Lorentz Group | 143 |
3.2 | Spin Space | 161 |
3.3 | Spinor Algebra | 170 |
3.4 | Spinors and World Vectors | 178 |
3.5 | Bivectors and Null Flags | 188 |
3.6 | The Electromagnetic Field (Revisited) | 196 |
Appendix A: Topologies For M | 210 | |
A.1 | The Euclidean Topology | 210 |
A.2 | E-Continuous Timelike Curves | 211 |
A.3 | The Path Topology | 215 |
Appendix B: Spinorial Objects | 226 | |
B.1 | Introduction | 226 |
B.2 | The Spinning Electron and Dirac's Demonstration | 227 |
B.3 | Homotopy in the Rotation and Lorentz Groups | 229 |
References | 240 | |
Symbols | 243 | |
Index | 251 |
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