Special relativity in the 21st century

Annalen der Physik (Leipzig)

Volumn 17, Issue 9-10, 2008, Pages 728-768

  Cacciatori, S ^a,b   Gorini, V ^a,b   Kamenshchik, A ^c,d  

^a UNIVERSITY OF INSUBRIA   (Italy)

^b INFN SEZIONE DI MILANO   (Italy)

^c INFN SEZIONE DI BOLOGNA   (Italy)

^d LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

Author keywords

De sitter group; General relativity; Minkowski; Minkowski hyperboloid; Special relativity

Indexed keywords

COSMOLOGY; GRAVITATION; SPECIAL EFFECTS;

DE SITTER GROUP; GENERAL RELATIVITY; MINKOWSKI; MINKOWSKI HYPERBOLOID; SPECIAL RELATIVITY;

RELATIVITY;

EID: 54949151983     PISSN: 00033804     EISSN: 15213889     Source Type: Journal    
DOI: 10.1002/andp.200810321     Document Type: Article

References (76)

1. H. Minkowski, Raum und Zeit, 80. Versammlung Deutscher Naturforscher (Köln, 1908). Published in Physikalische Zeitschrift 10, 104-111 (1909)
2. and Jahresbericht der Deutschen Mathematiker-Vereinigung 18, 75-88 (1909).
3. For an English translation, see H.A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl, The Principle of Relativity (Dover, New York, 1952).
4. A. Einstein, Zur Elektrodynamik bewegter Körper, Annalen der Physik 17, 891-921 (1905).
5. For an English translation, see H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl, The Principle of Relativity (Dover, New York, 1952).
6. W. A. vonlgnatowsky, Einige allgemeine Bemerkungen zum Relativitätsprinzip, Phys. Z. 11, 972-976 (1910).
7. J.-M. Lévy-Leblond, Une nouvelle limite non-relativiste du groupe de Poincaré, Ann. Inst. Henri Poincaré (A) Phys. Théor. 3, 1-12 (1965).
8. P. Frank and H. Rothe, Über die Transformation der Raumzeitkoordinaten von ruhenden auf bewegte Systeme, Annalen der Physik 34, 825-853 (1911).
9. V. Lalan, Sur les postulates qui sont à la base des cinématiques, Bull. Soc. Math. France 65, 83-99 (1937).
10. J.-M. Lévy-Leblond, One more derivation of thé Lorentz transformation, Am. J. Phys. 43, 271-277 (1976).
11. V. Gorini, Linear Kinematical Groups, Commun. Math. Phys. 21, 150-163 (1971).
12. A. Sen, How Galileo could have derived the special theory of relativity, Am. J. Phys. 62, 157-162 (1994).
13. D. Giulini, Algebraic and geometric structures of Special Relativity, Lect. Notes Phys. 702, 45 (2006).
14. Z. K. Silagadze, Relativity without tears, Acta Phys. Polon. B 39, 811-885 (2008).
15. F.J. Dyson, Missed opportunities, Bull. Am. Math. Soc. 78, 635-652 (1972).
16. H. Bacry and J.-M. Lévy-Leblond, Possible Kinematics, J. Math. Phys. 9, 1605-1614 (1968).
17. S. Perlmutter et al., Measurements of omega and lambda from 42 high-redshift supernovae, Astrophys. J. 517, 565-586, (1999);
18. A.G. Riess et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116, 1009-1038, (1998);
19. A. G. Riess et al., The farthest known supernova: Support for an accelerating universe and a glimpse of the epoch of deceleration, Astrophys. J. 560, 49-71 (2001);
20. D.N. Spergel et al., First year Wilkinson microwave anisotropy probe observations: Determination of cosmological parameters, Astrophys. J. Suppl. 148, 175 (2003).
21. Ya. B. Zeldovich, Cosmological Constant and Elementary Particles, JETP Lett. 6, 316 (1967);
22. Ya. B. Zeldovich, The cosmological constant and the theory of elementary particles, Sov. Phys. - Uspekhi 11, 381-393 (1968).
23. E. Cremmer, S. Ferrara, C. Kounnas, and D. V. Nanopoulos, Naturally vanishing cosmological constant in N = 1 supergravity, Phys. Lett. B 133, 61-66 (1983);
24. M. Visser, Sakharov's induced gravity: A modern perspective, Mod. Phys. Lett. A 17, 977-991 (2002);
25. A. Yu. Kamenshchik, A. Tronconi, G. P. Vacca, and G. Venturi, Vacuum energy and spectral function sum rules, Phys. Rev. D 75, 083514 (2007).
26. R.R. Caldwell, Dark energy, Physics World 17 (5), 37-42 (2004);
27. C.J. Conselice, The universe's invisible hand, Scientific American, pp. 24-31, February (2007);
28. E. Linde, S. Perlmutter, Dark energy: the decade ahead, Physics World 20 (12), 24-30 (2007).
29. R.R. Caldwell, An introduction to quintessence, Braz. J. Phys. 30, 215 (2000).
30. E. J. Copeland, M. Sami, and S. Tsujikawa, Dynamics of dark energy, Int. J. Mod. Phys. D 15, 1753 (2006).
31. A.O. Barvinsky, Covariant long-distance modifications of Einstein theory and strong coupling problem, Phys. Rev. D 71, 084007 (2005).
32. E. W. Kolb, S. Matarrese, and A. Riotto, On cosmic acceleration without dark energy, New J. Phys. 8, 322 (2006).
33. D.L. Wiltshire, Dark energy without dark energy, contributed to 6th International Heidelberg Conference on Dark Matter in Astro and Particle Physics, Sydney, Australia, 24-28 Sep 2007, e-Print: arXiv:0712.3984;
34. D. L. Wiltshire, Cosmic clocks, cosmic variance and cosmic averages, New J. Phys. 9, 377 (2007);
35. D.L. Wiltshire, Exact solution to the averaging problem in cosmology, Phys. Rev. Lett. 99, 251101 (2007);
36. B. M. Leith, S. C. C. Ng, and D.L. Wiltshire, Gravitational energy as dark energy: concordance of cosmological tests, Astrophys. J. 672, L91-L94 (2008).
37. J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (Oxford University Press, New York, 1986).
38. W. de Sitter, On the curvature of space, Proc. Kon. Ned. Akad. Wet. 20, 229 (1917).
39. L.H. Thomas, The motion of the spinning electron, Nature London 117, 514 (1926);
40. L.H. Thomas, The kinematics of an electron with an axis, Phil. Mag. 3, 1-21 (1927).
41. G. Lemaitre, Note on the de Sitter universe, J. Math. Phys. (MIT) 4, 188-192 (1925).
42. K. Lanczos, Bemerkungen zur de Sitterschen Welt, Phys. Z. 23, 539-543 (1922).
43. E. Inönü and E. P. Wigner, On the contraction of groups and their representations, Proc. Natl. Acad. Sci. (USA) 39, 510-524 (1953);
44. E. Saletan, Contraction of Lie Groups, J. Math. Phys. 2, 1-21 (1961);
45. M. Levy-Nahas, Deformation and Contraction of Lie Algebras, J. Math. Phys. 8, 1211-1222 (1967).
46. S. Cacciatori, V. Gorini, A. Kamcnshchik, and U. Moschella, Conservation laws and scattering for de Sitter classical particles, Class. Quantum Gravity 25, 075008 (2008).
47. F.G. Gürsey, Introduction to the de Sitter group in Group Theoretical Concepts and Methods in Elementary Particle Physics, edited by R G. Gürsey (Gordon and Breach, New York, 1964).
48. L. E Abbott and S. Deser, Stability of gravity with a cosmological constant, Nucl. Phys. B 195, 76-96 (1982).
49. A. Friedmann, Über die Krümmung des Raumes, Z. Phys. 10, 377-386 (1922).
50. English translation in Gen. Rel. Grav. 31, 1991-2000 ( 1999);
51. A. Friedmann, Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes, Z. Phys. 21, 326-332 (1924).
52. English translation in Gen. Rel. Grav. 31, 2001-2008 (1999).
53. A. Einstein, Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie, Sitzungsberichte der Preussischen Akad. d. Wissenschaften (Berlin), 142-152 (1917).
54. For an English translation, see H.A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl, The Principle of Relativity (Dover, New York, 1952).
55. P. A. M. Dirac, The electron wave equation in de Sitter space, Ann. Math. 36, 657-669 (1935).
56. E. Schrödinger, Proc. Roy. Irish Acad. (Sec. A) 46, 25 (1940).
57. E. Schrödinger, Expanding Universes (Cambridge University Press, Cambridge, 1956).
58. C. Fronsdal, Elementary particles in a curved space, Rev. Mod. Phys. 37, 221-224 (1965).
59. P. Roman and J. J. Aghassi, Classical field theory and gravitation in a de Sitter world, J. Math. Phys. 7, 1273-1283 (1966).
60. O. Nachtmann, Quantum field theory in de Sitter space, Commun. Math. Phys. 6, 1-16 (1967).
61. R. Aldrovandi, J.P. Beltrán Almeida, and J.G. Pereira, de Sitter special relativity, Class. Quantum Gravity 24, 1385-1404 (2007);
62. R. Aldrovandi, J. P. Beltrán Almeida, and J. G. Pereira, Cosmological Term and Fundamental Physics, Int. J. Mod. Phys. D 13, 2241-2248 (2004).
63. H.-Y. Guo, C.-G. Huang, Z. Xu, and B. Zhou, On Beltrami Model of de Sitter Spacetime, Mod. Phys. Lett. A 19, 1701-1710 (2004);
64. H.-Y. Guo, C.-G. Huang, Z. Xu, and B. Zhou, On special relativity with cosmological constant, Phys. Lett. A 331, 1-7 (2004);
65. H.-Y. Guo, On principle of inertia in closed universe, Phys. Lett. B 653, 88-94 (2007).
66. N.D. Birrell and P. C.W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1982).
67. J. Bros, H. Epstein, and U. Moschella, The lifetime of a massive particle in a de Sitter universe, J. Cosmology and Astropart. Phys. 02, 003 (2008).
68. J. Bros, H. Epstein, and U. Moschella, Analiticity properties and thermal effects for general quantum field theory on de Sitter space-time, Commun. Math. Phys. 196, 535-570 (1996).
69. J. Bros, J.-P. Gazeau, and U. Moschella, Quantum Field Theory in de Sitter Universe, Phys. Rev. Lett. 73, 1746-1749 (1994).
70. R. Haag, N.M. Hugenholtz, and M. Winnink, On the equilibrium states in quantum statistical mechanics, Commun. Math. Phys. 5, 215-236 (1967).
71. G.W. Gibbons and S.W. Hawking, Cosmological event horizon, thermodynamics and particle creation, Phys. Rev. D 10, 2738-2751 (1977).
72. S.W. Hawking, Particle creation by Black Holes, Commun. Math. Phys. 43, 199-220 (1975).
73. W. Unruh, Notes on black-hole evaporation, Phys. Rev. D 14, 870-892 (1976).
74. A.D. Linde, Particle physics and inflationary cosmology, e-print: hep-th/0503203.
75. L.M. Krauss and R.J. Scherrer, The end of cosmology?, Scientific American, pp. 34-41, March (2008).
76. F.W. Hehl and Y.N. Obukhov, Élie Cartan's torsion in geometry and in field theory, an essay, e-print: arXiv:0711.1535.