Axiomatic relativity theory

摘要

CONTENTSIntroductionChapter I. Space-time geometry§ 1. The concept of space-time§ 2. Notation and definitions§ 3. The continuity theorem§ 4. Contingency theorems§ 5. The mapping of cones§ 6. The geometry of space-time§ 7. Micro-causality and the geometry of space-time§ 8. Time-like Minkowsky space§ 9. Lorentz and Galilean kinematics§ 10. An axiomatic definition of the Galili and Lorentz groupsChapter II. Mappings of families of cones in an affine space§ 11. Mappings of elliptic cones§ 12. Conformal space§ 13. The simplest axiomatizations of space-time§ 14. Theorems on finitely many light sources§ 15. Mappings of strictly convex cones§ 16. How many interial systems of reference?§ 17. The axiomatics of relativity theory§ 18. Mappings of arbitrary cones§ 19. Mappings of discrete cones§ 20. Mappings of pseudo-Euclidean spacesChapter III. Connected pre-orders in an affine space§ 21. Maps of ordered spaces§ 22. Connected pre-orders§ 23. Cones with a transitive groupChapter IV. The chronogeometry of spaces§ 24. Spaces with a non-commutative group§ 25. Mappings of cones in Lobachevskii space§ 26. The chronogeometry of Lorentz manifolds§ 27. An analogue of Aleksandrov's theorem in the cla