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

by Naber, Gregory L.

• ISBN13: 9780486432359
• ISBN10: 0486432351
• Format: Paperback
• Copyright: 2003-12-29
• Publisher: Dover Publications

Summary

This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; the theory of spinors; and more. 1992 edition. 43 figures.

Author Biography

Gregory L. Naber: California State University

Table of Contents

Preface	v
Acknowledgments	xi
Introduction	1	(6)
Chapter 1 Geometrical Structure of M	7	(93)
1.1 Preliminaries	7	(2)
1.2 Minkowski Spacetime	9	(6)
1.3 The Lorentz Group	15	(31)
1.4 Timelike Vectors and Curves	46	(15)
1.5 Spacelike Vectors	61	(3)
1.6 Causality Relations	64	(10)
1.7 Spin Transformations and the Lorentz Group	74	(13)
1.8 Particles and Interactions	87	(13)
Chapter 2 Skew-Symmetric Linear Transformations and Electromagnetic Fields	100	(43)
2.1 Motivation via the Lorentz Law	100	(1)
2.2 Elementary Properties	101	(6)
2.3 Invariant Subspaces	107	(6)
2.4 Canonical Forms	113	(4)
2.5 The Energy-Momentum Transformation	117	(4)
2.6 Motion in Constant Fields	121	(5)
2.7 Variable Electromagnetic Fields	126	(17)
Chapter 3 The Theory of Spinors	143	(67)
3.1 Representations of the Lorentz Group	143	(18)
3.2 Spin Space	161	(9)
3.3 Spinoy Algebra	170	(8)
3.4 Spinors and World Vectors	178	(10)
3.5 Bivectors and Null Flags	188	(8)
3.6 The Electromagnetic Field (Revisited)	196	(14)
Appendix A Topologies For M	210	(16)
A.1 The Euclidean Topology	210	(1)
A.2 E-Continuous Timelike Curves	211	(4)
A.3 The Path Topology	215	(11)
Appendix B Spinorial Objects	226	(14)
B.1 Introduction	226	(1)
B.2 The Spinning Electron and Dirac's Demonstration	227	(2)
B.3 Homotopy in the Rotation and Lorentz Groups	229	(11)
References	240	(3)
Symbols	243	(8)
Index	251