Variations on the seventh route to relativity

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 68, Issue 10, 2003, Pages

  Anderson, Edward ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

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EID: 85039021304     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.68.104001     Document Type: Article

References (87)

1. A. Einstein, Ann. Phys. (Leipzig) 49, 769 (1916)[the English translation is available in The Principle of Relativity (Dover, New York, 1952), formerly published by (Methuen, London, 1923)].
2. E. Cartan, J. Math. Pures Appl. 1, 141 (1922).
3. H. Weyl, Space-Time-Matter, 4th ed. (English translation: Methuen, London, 1920), wherein note 8 of Chap. 4 lists the original literature for the Einstein-Hilbert action.
4. D. Lovelock, J. Math. Phys. 12, 498 (1971).
5. R. Arnowitt, S. Deser, and C.W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
6. C.W. Misner, K. Thorne, and J.A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
7. J.A. Wheeler, in Battelle Rencontres: 1967 Lectures in Mathematics and Physics, edited by C.M. DeWitt and J.A. Wheeler (Benjamin, New York, 1968).
8. M. Fierz and W. Pauli, Proc. R. Soc. London A173, 211 (1939).
9. A.D. Sakharov, Sov. Phys. Dokl. 12, 1040 (1968).
10. M.B. Green, J.H. Schwartz, and E. Witten, Superstring Theory (Cambridge University Press, Cambridge, England, 1987).
11. See, for example, A. Ashtekar, Lectures on Nonperturbative Canonical Gravity (World Scientific, Singapore, 1991).
12. See, for example, L. Witten, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
13. See, for example, M.J. Duff, hep-th/9410046, and references therein.
14. H. Weyl, Sitzungsber. K. Preuss. Akad. Wiss. 26, 465 (1918), available in English translation in same book as 1.
15. C. Brans and R. Dicke, Phys. Rev. 124, 925 (1961).
16. S.A. Hojman, K. Kuchař, and C. Teitelboim, Ann. Phys. (N.Y.) 96, 88 (1976).
17. J. Barbour, B.Z. Foster, and N. Ó Murchadha, Class. Quantum Grav. 19, 3217 (2002).
18. K. Kuchař, J. Math. Phys. 15, 708 (1974).
19. S.A. Hojman and K. Kuchař, Bull. Am. Phys. Soc. 17, 450 (1972);K. Kuchař, in Relativity, Astrophysics and Cosmology, edited by W. Israel (Reidel, Dordrecht, 1973);
20. S.A. Hojman, K. Kuchař, and C. Teitelboim, Nature (London) 245, 97 (1973).
21. C. Teitelboim, in General Relativity and Gravitation, Vol. 1, edited by A. Held (Plenum, New York, 1980).
22. J.A. Wheeler, Geometrodynamica (Academic, New York, 1962).
23. P.A.M. Dirac, Lectures on Quantum Mechanics (Yeshiva University, New York, 1964).
24. E. Anderson and J. Barbour, Class. Quantum Grav. 19, 3249 (2002).
25. J. Barbour and B. Bertotti, Proc. R. Soc. London A382, 295 (1982).
26. J. Barbour, Class. Quantum Grav. 11, 2853 (1994).
27. R.F. Baierlein, D. Sharp, and J.A. Wheeler, Phys. Rev. 126, 1864 (1962).
28. K. Kuchař, J. Math. Phys. 17, 777 (1976);
29. J. Math. Phys.K. Kuchař17, 792 (1976);
30. J. Math. Phys.K. Kuchař17, 801 (1976);
31. J. Math. Phys.K. Kuchař18, 1589 (1977).
32. B.S. DeWitt, Phys. Rev. 160, 1113 (1967).
33. E. Anderson, gr-qc/0205118.
34. C.J. Isham, Proc. R. Soc. London A351, 209 (1976);
35. M. Henneaux, Bull. Soc. Math. Belg. 31, 47 (1979);
36. C. Teitelboim, Phys. Rev. D 25, 3159 (1982);
37. Phys. Rev. DM. Pilati, 26, 2645 (1982);
38. Phys. Rev. DM. Pilati28, 729 (1983);
39. Phys. Rev. DG. Francisco and M. Pilati, 31, 241 (1985).
40. J. Barbour and N. Ó Murchadha, gr-qc/9911071.
41. E. Anderson, J. Barbour, B.Z. Foster, and N. Ó Murchadha, Class. Quantum Grav. 20, 1571 (2003).
42. J. Barbour, Class. Quantum Grav. 20, 1543 (2003).
43. E. Anderson, J. Barbour, B.Z. Foster, B. Kelleher, and N. Ó Murchadha (to be published).
44. J.W. York, Phys. Rev. Lett. 28, 1082 (1972);
45. J.W. YorkJ. Math. Phys. 14, 456 (1973);
46. J.W. YorkAnn. Inst. Henri Poincaré, Sect. A 21, 319 (1974).
47. J. Barbour, B.Z. Foster, and N. Ó Murchadha (to be published).
48. J.N. Butterfield, Br. J. Philos. Sci. (to be published), gr-qc/0103055.
49. L. Smolin, in Time and the Instant, edited by R. Durie (Clinamen Press, Manchester, 2000).
50. C. Lanczos, The Variational Principles of Mechanics (University of Toronto Press, Toronto, 1949).
51. G.S. Asanov, Finsler Geometry, Relativity and Gauge Theories (Reidel, Dordrecht, 1985).
52. J. Barbour, Class. Quantum Grav. 11, 2875 (1994);The End of Time (Oxford University Press, Oxford, 1999).
53. See, for example, E.T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, 1904).
54. C.W. Misner, in Magic Without Magic: John Archibald Wheeler, edited by J.R. Klauder (Freeman, San Francisco, 1972).
55. B.S. DeWitt, in Relativity, Proceedings of the Relativity Conference in the Midwest, Cincinnati, Ohio, 1969, edited by M. Carmeli, S.I. Fickler, and L. Witten (Plenum, New York, 1970); see also A.E. Fischer’s contribution to the same proceedings.
56. E.P. Belasco and H.C. Ohanian, J. Math. Phys. 10, 1053 (1969);
57. R. Bartnik and G. Fodor, Phys. Rev. D 48, 3596 (1993).
58. D. Giulini, J. Math. Phys. 40, 2470 (1999).
59. V.A. Belinskii, I.M. Khalatnikov, and E.M. Lifshitz, Adv. Phys. 19, 525 (1970);
60. C.W. Misner, Phys. Rev. 186, 1319 (1969).
61. J. Isenberg and V. Moncrief, Ann. Phys. 199, 84 (1990);
62. B.K. Berger, gr-qc/9801010;Living Rev. Relativity 1 (2002).
63. A. Burd and R. Tavakol, Phys. Rev. D 47, 5336 (1993).
64. M. Szydlowski and A. Lapeta, Phys. Lett. A 148, 239 (1990).
65. K. Kuchař, in Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics, edited by G. Kunstatter, D. Vincent, and J. Williams (World Scientific, Singapore, 1992);C.J. Isham, in Integrable Systems, Quantum Groups and Quantum Field Theories, edited by L.A. Ibort and M.A. Rodríguez (Kluwer, Dordrecht, 1993).
66. K.S. Stelle, Gen. Relativ. Gravit. 9, 353 (1978);
67. I.L. Buchbinder and S.L. Lyahovich, Class. Quantum Grav. 4, 1487 (1987).
68. See, for example, M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory (Perseus, Reading, MA, 1995).
69. C. Kiefer, Phys. Lett. B 225, 227 (1989).
70. N. Ó Murchadha, Int. J. Mod. Phys. A 20, 2717 (2002).
71. R. Penrose and W. Rindler, Spinors and Space-time Vol. 1 Two-Spinor Calculus and Relativistic Fields (Cambridge University Press, Cambridge, England, 1984).
72. J. Géhéniau and M. Henneaux, Gen. Relativ. Gravit. 8, 611 (1977).
73. Y. Kosmann, Ann. Mat. Pura Appl. (IV) XCI, 330 (1972).
74. P.A.M. Dirac, in Recent Developments in General Relativity (Pergamon, Oxford, 1962).
75. J.E. Nelson and C. Teitelboim, Phys. Lett. 69B, 81 (1977).
76. S. Deser, J.H. Kay, and K.S. Stelle, Phys. Rev. D 16, 2448 (1977);
77. E.S. Fradkin and M.A. Vasiliev, Phys. Lett. 72B, 70 (1977);
78. M. Pilati, Nucl. Phys. B132, 138 (1978);
79. P.D. D’Eath, Phys. Rev. D 29, 2199 (1984);Supersymmetric Quantum Cosmology (Cambridge University Press, Cambridge, England, 1996);
80. T. Jacobson, Class. Quantum Grav. 5, 923 (1988).
81. S. Weinberg, Quantum Theory of Fields, Vol. III (Cambridge University Press, Cambridge, England, 2000).
82. C. Teitelboim, Phys. Rev. Lett. 38, 1106 (1977).
83. The most recent confirmation that we are aware of that this work remains incomplete is on p. 96 of D’Eath’s book in 61.
84. I. Kouletsis, gr-qc/9801019.
85. K.N. Savvidou, J. Math. Phys. 43, 3053 (2002);
86. K.N. SavvidouClass. Quantum Grav. 18, 3611 (2001);
87. I. Kouletsis and K. Kuchař, Phys. Rev. D 65, 125026 (2002).