Abstract space–times and their Lorentz groups

Journal of Mathematical Physics

Volumn 37, Issue 6, 1996, Pages 3073-3098

  Smith, Jonathan D H ^a   Ungar, Abraham A ^b  

^a IOWA STATE UNIVERSITY   (United States)

^b NORTH DAKOTA STATE UNIVERSITY   (United States)

Author keywords

GROUP THEORY; LORENTZ GROUPS; RELATIVITY THEORY; SPACE TIME

Indexed keywords

EID: 0345985444     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531555     Document Type: Article

References (23)

1. A. A. Ungar, “Thomas precession and its associated grouplike structure,” Am. J. Phys. 59, 824–834 (1991).AJPIAS
2. A. A. Ungar, “The abstract Lorentz transformation group,” Am. J. Phys. 60, 815–828 (1992).AJPIAS
3. H. Wefelscheid, On K-loops, J. Geom. 44, 22–23 (1992)
4. H. Wefelscheid, 53, 26 (1995).
5. H. Karzel, Inzidenzgruppen I, Lecture notes by I. Pieper and K. Sörensen (University of Hamburg, Hamburg, 1965) pp. 123–135
6. H. Karzel, “Zusammenhänge zwischen Fastbereichen, scharf 2-fach transitiven Permutationsgruppen und 2-Strukturen mit Rechtecksaxiom,” Abh. Math. Sem. Univ. Hamburg 32, 191–206 (1968).
7. R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and all that (Benjamin, New York, 1964); and G. Kaiser, Quantum Physics, Relativity and Complex Spacetime: Towards a New Synthesis, North-Holland Mathematics Studies, Vol. 163 (North-Holland, Amsterdam, New York, 1990).
8. H. Wähling, Theorie der Fastkörper (Thales Verlag, W. Germany, 1987).
9. A. A. Ungar, “The abstract complex Lorentz transformation group with real metric I: Special relativity formalism to deal with the holomorphic automorphism group of the unit ball in any complex Hilbert space,” J. Math. Phys. 35, 1408–1425 (1994); JMAPAQ
10. A. A. Ungar, “Erratum: ‘The abstract complex Lorentz transformation group with real metric I: Special relativity formalism to deal with the holomorphic automorphism group of the unit ball in any complex Hilbert space,’” J. Math. Phys. 35, 3770 (1994).JMAPAQ
11. A. A. Ungar, “The abstract complex Lorentz transformation group with real metric II: The invariance group of the form [formula omitted],” J. Math. Phys. 35, 1881–1913 (1994).JMAPAQ
12. For a recent article about the cocycle equation and its relevance, see B. R. Ebanks and C. T. Ng, “On generalized cocycle equations,” Aequat. Math. 46, 76–90 (1993).AEMABN
13. A. A. Ungar, “The expanding Minkowski space,” Results Math. 17, 342–354 (1990).
14. A. A. Ungar, “Extension of the unit disk gyrogroup into the unit ball of any real inner product space,” J. Math. Anal. Appl. (in press).
15. This article is based on the use of a gyrogroup introduced in A. A. Ungar, “The holomorphic automorphism group of the complex disk,” Aequat. Math. 47, 240–254 (1994).AEMABN
16. Y. You and A. A. Ungar, “Equivalence of two gyrogroup structures on unit balls,” Results Math. 28, 359–371 (1995).
17. A. A. Ungar, “Midpoints in gyrogroups” (preprint).
18. H. Urbantke, “Comment on ‘The expanding Minkowski space’ by A. A. Ungar,” Results Math. 19, 189–191 (1991).
19. A. A. Ungar, “Weakly associative groups,” Results Math. 17, 149–168 (1990).
20. O. Chein, H. O. Pflugfelder, and J. D. H. Smith (eds.), Quasigroups and Loops Theory and Applications, Sigma Series in Pure Mathematics (Heldermann-Verlag, Berlin, 1990), Vol. 8.
21. A. Kreuzer, “Beispiele endlicher und unendlicher K-loops,” Results Math. 23, 355–362 (1993)
22. B. Scirnemi, “Cappi di Bruck e loro generalizzazioni,” Rend. Sem. Mat. Univ. Padova 60, 141–149 (1978).
23. See, e.g., G. Karpilovsky, The Schur Multiplier (Clarendon, Oxford, 1987).