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The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity Book

The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity
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  • The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity
  • Written by author Gregory L. Naber
  • Published by Springer-Verlag New York, LLC, January 1992
  • This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustome
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Authors

Preface
Acknowledgments
Introduction1
Ch. 1Geometrical Structure of M7
1.1Preliminaries7
1.2Minkowski Spacetime9
1.3The Lorentz Group15
1.4Timelike Vectors and Curves46
1.5Spacelike Vectors61
1.6Causality Relations64
1.7Spin Transformations and the Lorentz Group74
1.8Particles and Interactions87
Ch. 2Skew-Symmetric Linear Transformations and Electromagnetic Fields100
2.1Motivation via the Lorentz Law100
2.2Elementary Properties101
2.3Invariant Subspaces107
2.4Canonical Forms113
2.5The Energy-Momentum Transformation117
2.6Motion in Constant Fields121
2.7Variable Electromagnetic Fields126
Ch. 3The Theory of Spinors143
3.1Representations of the Lorentz Group143
3.2Spin Space161
3.3Spinor Algebra170
3.4Spinors and World Vectors178
3.5Bivectors and Null Flags188
3.6The Electromagnetic Field (Revisited)196
Appendix A: Topologies For M210
A.1The Euclidean Topology210
A.2E-Continuous Timelike Curves211
A.3The Path Topology215
Appendix B: Spinorial Objects226
B.1Introduction226
B.2The Spinning Electron and Dirac's Demonstration227
B.3Homotopy in the Rotation and Lorentz Groups229
References240
Symbols243
Index251


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