Trigonometry of spacetimes: A new self-dual approach to a curvature/signature (in)dependent trigonometry

Journal of Physics A: Mathematical and General

Volumn 33, Issue 24, 2000, Pages 4525-4551

  Herranz, Francisco J ^a   Ortega, Ramón ^b   Santander, Mariano ^b  

^a UNIVERSITY OF BURGOS   (Spain)

^b UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034705244     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/33/24/309     Document Type: Article

References (45)

1. Birman G S and Nomizu K 1984 Am. Math. Month. 91 543-9
2. Yaglom I M 1979 A Simple Non-Euclidean Geometry and its Physical Basis (New York: Springer)
3. Hsiang W-Y 1989 Ann. Global Anal. Geom. 7 29-45
4. Leuzinger 1992 Coment. Math. Helv. 67 252-92
5. Aslaksen H 1990 Trans. Am. Math. Soc. 317 127-42
6. Aslaksen H and Huynh H-L 1997 Laws of trigonometry in symmetric spaces Geometry from the Pacific Rim ed A J Berrick et al (Berlin: Walter de Gruyter) pp 23-6
7. Aslaksen H and Huynh H-L Laws of trigonometry in SU (3) and SL (3ℂ)/SU (3) Preprint National University of Singapore
8. Bonola 1955 Non-Euclidean geometry (New York: Dover)
9. Martin G E 1986 The Foundations of Geometry and the Non-Euclidean Plane (New York: Springer)
10. Ballesteros A, Herranz F J, del Olmo M A and Santander M 1993 J. Phys. A: Math. Gen. 26 5801-23
11. Herranz F J 1995 Grupos de Cayley-Klein clásicos y cuánticos PhD Thesis University of Valladolid
12. Ballesteros A, Herranz F J, del Olmo M A and Santander M 1995 J. Math. Phys. 36 631-40
13. Santander M and Herranz F J 1997 Int. J. Mod. Phys. A 12 99-107
14. Santander M and Herranz F J 1997 A Cayley-Klein scheme for all quasisimple real Lie algebras and Freudenthal magic squares Physical Applications and Mathematical Aspects of Geometry, Groups and Algebras vol 1, ed H-D Doebner et al (Singapore: World Scientific) pp 151-6
15. Herranz F J and Santander M 1997 J. Phys. A: Math. Gen. 30 5411-26
16. de Azcárraga J A, Herranz F J, Pérez Bueno J C and Santander M 1998 J. Phys. A: Math. Gen. 31 1373-94
17. Herranz F J and Santander M 1998 Homogeneous phase spaces: the Cayley-Klein framework Geometría y Física vol XXXII, ed J F Cariñena et al (Madrid: Real Academia de Ciencias) pp 59-84
18. Herranz F J and Santander M 1999 J. Phys. A: Math. Gen. 32 3743-54
19. Rañada M F and Santander M 1999 J. Math. Phys. 40 5026-57
20. Santander M 1999 Symmetric homogeneous spaces in classical and quantum mechanics: a viewpoint for classification Symmetries in Quantum Mechanics and Quantum Optics ed A Ballesteros et al (Burgos: University of Burgos) pp 335-52
21. Santander M, Division algebras and the classifications of simple Lie algebras and of symmetric homogeneous spaces, in preparation
22. Sommerville D M Y 1910 Proc. Edin. Math. Soc. 28 25-41
23. Yaglom I M, Rozenfel'd B A and Yasinskaya E U 1966 Sov. Math. Surveys 19 49
24. Ortega R and Santander M Trigonometry of the quantum space of states and Hermitian trigonometry, in preparation
25. Wang H C 1952 Ann. Math. 55 172-91
26. Inönü E and Wigner E P 1953 Proc. Natl Acad. Sci., USA 39 510 Inönü E and Wigner E P 1954 Proc. Natl Acad. Sci., USA 40 119
27. Inönü E and Wigner E P 1953 Proc. Natl Acad. Sci., USA 39 510 Inönü E and Wigner E P 1954 Proc. Natl Acad. Sci., USA 40 119
28. Bacry H and Lévy-Leblond J M 1968 J. Math, Phys. 9 1605
29. Berger M 1987 Geometry I, II (Berlin: Springer)
30. Ratcliffe J G 1994 Foundations of Hyperbolic Manifolds (New York: Springer)
31. Ramsay A and Richtmyer R D 1995 Introduction to Hyperbolic Geometry (New York: Springer)
32. Arnol'd V I 1995 Usp. Mat. Nauk 50 3-68 (Engl. transl. Russian Math. Surveys 50 1-68)
33. Arnol'd V I 1995 Usp. Mat. Nauk 50 3-68 (Engl. transl. Russian Math. Surveys 50 1-68)
34. Rozenfel'd B A 1988 A History of Non-Euclidean Geometry (New York: Springer)
35. Todhunter I (rev. Leathem J G) 1901 Spherical Trigonometry (London: Macmillan)
36. del Olmo M A and Santander M 1989 J. Phys. A: Math. Gen. 22 L763 del Olmo M A and Santander M 1990 J. Geom. Phys. 7 171
37. del Olmo M A and Santander M 1989 J. Phys. A: Math. Gen. 22 L763 del Olmo M A and Santander M 1990 J. Geom. Phys. 7 171
38. Lévy-Leblond J M 1977 Nuovo Cimento 7 187-214
39. Milnor J 1982 Bull. Am. Math. Soc. 6 9
40. Baxter R J 1983 Commun. Math. Phys. 88 185
41. Zamolodchikov A B 1981 Commun. Math. Phys. 79 489
42. Jimbo M (ed) 1989 Yang-Baxter Equation in Integrable Systems (Advanced Series in Mathematics and Physics, vol 10) (Singapore: World Scientific)
43. Jing-Ling Chen and Mo-Lin Ge 1998 J. Geom. Phys. 25 341-5
44. Ortega R and Santander M 1998 Geometry and Physics (Anales de Física Monografías, vol 5) ed M Asorey and J F Cariñena (Madrid: Ciemat and RSEF) p 209
45. Ortega R and Santander M 1999 Geometrical phases and trigonometry of the quantum space of states Symmetries in Quantum Mechanics and Quantum Optics ed A Ballesteros et al (Burgos: University of Burgos) pp 223-33