Probabilities in quantum cosmological models: A decoherent histories analysis using a complex potential

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 80, Issue 12, 2009, Pages

  Halliwell, J J ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 73449104204     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.80.124032     Document Type: Article

References (101)

1. J.J. Halliwell, in Quantum Cosmology and Baby Universes, edited by, S. Coleman, J.B. Hartle, T. Piran and, S. Weinberg, (World Scientific, Singapore, 1991), http://xxx.soton.ac.uk/abs/0909.2566. These introductory lectures on quantum cosmology contain a detailed account of the WKB interpretation.
2. C. Kiefer and B. Sandhoefer, arXiv:gr-qc/0804.0672;
3. D.L. Wiltshire, arXiv:gr-qc/0101003.
4. J.B. Hartle, S.W. Hawking, and T. Hertog, Phys. Rev. D PRVDAQ 1550-7998 77, 123537 (2008); 10.1103/PhysRevD.77.123537
5. J.B. Hartle S.W. Hawking T. Hertog Phys. Rev. Lett. 100, 201301 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.201301 (Pubitemid 351748236)
6. B. DeWitt, in Gravitation: An Introduction to Current Research, edited by, L. Witten, (John Wiley and Sons, New York, 1962).
7. C. Rovelli, Classical Quantum Gravity CQGRDG 0264-9381 8, 297 (1991); 10.1088/0264-9381/8/2/011
8. C. Rovelli Classical Quantum Gravity CQGRDG 0264-9381 8, 317 (1991); 10.1088/0264-9381/8/2/012
9. C. Rovelli Phys. Rev. D PRVDAQ 0556-2821 42, 2638 (1990); 10.1103/PhysRevD.42.2638
10. C. Rovelli Phys. Rev. D PRVDAQ 0556-2821 43, 442 (1991); 10.1103/PhysRevD.43.442
11. D. Marolf, Classical Quantum Gravity CQGRDG 0264-9381 12, 1199 (1995); 10.1088/0264-9381/12/5/011
12. D. Marolf Classical Quantum Gravity CQGRDG 0264-9381 12, 1441 (1995); 10.1088/0264-9381/12/6/010
13. P. Hajicek, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 36, 4612 (1995); 10.1063/1.530911
14. M. Montesinos, C. Rovelli, and T. Thiemann, Phys. Rev. D PRVDAQ 0556-2821 60, 044009 (1999); 10.1103/PhysRevD.60.044009
15. M. Montesinos, Gen. Relativ. Gravit. 33, 1 (2001); GRGVA8 0001-7701 10.1023/A:1002067601136
16. R. Gambini and R.A. Porto, Phys. Rev. D PRVDAQ 0556-2821 63, 105014 (2001). 10.1103/PhysRevD.63.105014 (Pubitemid 33795180)
17. K. Kuchar, arXiv:gr-qc/9304012;
18. K. Kuchar 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);
19. C. Isham, arXiv:gr-qc/9210011.
20. S.W. Hawking, Nucl. Phys. NUPBBO 0550-3213 B239, 257 (1984). 10.1016/0550-3213(84)90093-2
21. J.B. Hartle, in Proceedings of the 1992 Les Houches School, Gravity and its Quantizations, edited by, B. Julia, and, J. Zinn-Justin, (Elsevier, New York, 1995).
22. J.B. Hartle and D. Marolf, Phys. Rev. D PRVDAQ 0556-2821 56, 6247 (1997). 10.1103/PhysRevD.56.6247
23. J.J. Halliwell and J. Thorwart, Phys. Rev. D PRVDAQ 0556-2821 64, 124018 (2001). 10.1103/PhysRevD.64.124018
24. J.J. Halliwell and J. Thorwart, Phys. Rev. D PRVDAQ 0556-2821 65, 104009 (2002). 10.1103/PhysRevD.65.104009 (Pubitemid 44628368)
25. J.J. Halliwell and P. Wallden, Phys. Rev. D PRVDAQ 1550-7998 73, 024011 (2006). 10.1103/PhysRevD.73.024011
26. D. Craig and J.B. Hartle, Phys. Rev. D PRVDAQ 0556-2821 69, 123525 (2004). 10.1103/PhysRevD.69.123525 (Pubitemid 44653861)
27. J. Whelan, Phys. Rev. D PRVDAQ 0556-2821 50, 6344 (1994). 10.1103/PhysRevD.50.6344
28. C. Anastopoulos and K. Savvidou, Classical Quantum Gravity CQGRDG 0264-9381 17, 2463 (2000); 10.1088/0264-9381/17/13/301
29. C. Anastopoulos K. Savvidou Classical Quantum Gravity CQGRDG 0264-9381 22, 1841 (2005). 10.1088/0264-9381/22/9/023 (Pubitemid 41238055)
30. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao, and T. Thiemann, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 36, 6456 (1995); 10.1063/1.531252
31. A. Higuchi, Classical Quantum Gravity CQGRDG 0264-9381 8, 1983 (1991); 10.1088/0264-9381/8/11/010
32. D. Giulini and D. Marolf, Classical Quantum Gravity CQGRDG 0264-9381 16, 2489 (1999); 10.1088/0264-9381/16/7/322
33. D. Giulini D. Marolf Classical Quantum Gravity CQGRDG 0264-9381 16, 2479 (1999); 10.1088/0264-9381/16/7/321
34. F. Embacher, Hadronic J. 21, 337 (1998); HAJODX 0162-5519
35. N. Landsmann, J. Geom. Phys. 15, 285 (1995); JGPHE5 0393-0440 10.1016/0393-0440(94)00034-2
36. D. Marolf, arXiv:gr-qc/0011112.
37. M. Gell-Mann and J.B. Hartle, in Complexity, Entropy and the Physics of Information, SFI Studies in the Sciences of Complexity, edited by, W. Zurek, (Addison Wesley, Reading, MA, 1990), Vol. 8;
38. and in Proceedings of the Third International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, edited by, S. Kobayashi, H. Ezawa, Y. Murayama and, S. Nomura, (Physical Society of Japan, Tokyo, 1990).
39. M. Gell-Mann and J.B. Hartle, Phys. Rev. D PRVDAQ 0556-2821 47, 3345 (1993). 10.1103/PhysRevD.47.3345
40. R.B. Griffiths, J. Stat. Phys. 36, 219 (1984); JSTPSB 0022-4715 10.1007/BF01015734
41. R.B. Griffiths Phys. Rev. Lett. 70, 2201 (1993); PRLTAO 0031-9007 10.1103/PhysRevLett.70.2201
42. R.B. Griffiths Phys. Rev. A 54, 2759 (1996); PLRAAN 1050-2947 10.1103/PhysRevA.54.2759
43. R.B. Griffiths Phys. Rev. A 57, 1604 (1998). PLRAAN 1050-2947 10.1103/PhysRevA.57.1604
44. R. Omnès, J. Stat. Phys. 53, 893 (1988); JSTPSB 0022-4715 10.1007/BF01014230
45. R. Omnès J. Stat. Phys. 53, 933 (1988); JSTPSB 0022-4715 10.1007/BF01014231
46. R. Omnès J. Stat. Phys. 53, 957 (1988); JSTPSB 0022-4715 10.1007/BF01014232
47. R. Omnès J. Stat. Phys. 57, 357 (1989); JSTPSB 0022-4715 10.1007/BF01023649
48. R. Omnès Ann. Phys. (N.Y.) APNYA6 0003-4916 201, 354 (1990); 10.1016/0003-4916(90)90045-P
49. R. Omnès Rev. Mod. Phys. 64, 339 (1992). RMPHAT 0034-6861 10.1103/RevModPhys.64.339
50. R. Omnès, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 38, 697 (1997). 10.1063/1.531886 (Pubitemid 127025171)
51. J.J. Halliwell, in Fundamental Problems in Quantum Theory, edited by, D. Greenberger, and, A. Zeilinger, Annals of the New York Academy of Sciences Vol. 775 (New York Academy of Sciences, New York, 1994), p. 726.
52. J.J. Halliwell, arXiv:quant-ph/0301117.
53. J.J. Halliwell, Phys. Rev. D PRVDAQ 0556-2821 60, 105031 (1999). 10.1103/PhysRevD.60.105031 (Pubitemid 40647503)
54. C. Isham, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 35, 2157 (1994); 10.1063/1.530544 (Pubitemid 24782858)
55. C. Isham and N. Linden, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 35, 5452 (1994); 10.1063/1.530759 (Pubitemid 24823399)
56. C. Isham N. Linden J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 36, 5392 (1995). 10.1063/1.531267
57. J.J. Halliwell, Nucl. Phys. NUPBBO 0550-3213 B266, 228 (1986); 10.1016/0550-3213(86)90182-3
58. J.J. Halliwell Nucl. Phys. NUPBBO 0550-3213 B286, 729 (1987). 10.1016/0550-3213(87)90461-5
59. J.J. Halliwell, Phys. Rev. D PRVDAQ 0556-2821 38, 2468 (1988); 10.1103/PhysRevD.38.2468
60. J.J. Halliwell and J.B. Hartle, Phys. Rev. D PRVDAQ 0556-2821 41, 1815 (1990); 10.1103/PhysRevD.41.1815
61. J.J. Halliwell J.B. Hartle Phys. Rev. D PRVDAQ 0556-2821 43, 1170 (1991); 10.1103/PhysRevD.43.1170
62. C. Teitelboim, Phys. Rev. D PRVDAQ 0556-2821 25, 3159 (1982); 10.1103/PhysRevD.25.3159
63. C. Teitelboim Phys. Rev. D PRVDAQ 0556-2821 28, 297 (1983). 10.1103/PhysRevD.28.297
64. J.J. Halliwell, Phys. Rev. D PRVDAQ 0556-2821 36, 3626 (1987). 10.1103/PhysRevD.36.3626
65. See the collection of articles in the volume Time in Quantum Mechanics, edited by, J.G. Muga, R. Sala Mayato and, I.L. Egusquiza, (Springer, Berlin, 2002);
66. J.G. Muga and C.R. Leavens, Phys. Rep. 338, 353 (2000). PRPLCM 0370-1573 10.1016/S0370-1573(00)00047-8
67. J.G. Muga, S. Brouard, and D. Macias, Ann. Phys. (N.Y.) APNYA6 0003-4916 240, 351 (1995); 10.1006/aphy.1995.1048
68. Ph. Blanchard and A. Jadczyk, Helv. Phys. Acta 69, 613 (1996); HPACAK 0018-0238
69. J.P. Palao, J.G. Muga, S. Brouard, and A. Jadczyk, Phys. Lett. A 233, 227 (1997); PYLAAG 0375-9601 10.1016/S0375-9601(97)00466-0
70. A. Ruschhaupt, J. Phys. A JPHAC5 0305-4470 35, 10429 (2002); 10.1088/0305-4470/35/48/314 (Pubitemid 37049450)
71. J.G. Muga, J.P. Palao, B. Navarro, and I.L. Egusquiza, Phys. Rep. 395, 357 (2004); PRPLCM 0370-1573 10.1016/j.physrep.2004.03.002 (Pubitemid 38561918)
72. J.J. Halliwell, Prog. Theor. Phys. 102, 707 (1999). PTPKAV 0033-068X 10.1143/PTP.102.707
73. J.J. Halliwell and J.M. Yearsley, Phys. Rev. A 79, 062101 (2009). PLRAAN 1050-2947 10.1103/PhysRevA.79.062101
74. J.J. Halliwell and Y. Yearsley, arXiv:quant-ph/0903.1958.
75. N. Yamada and S. Takagi, Prog. Theor. Phys. 85, 985 (1991); PTPKAV 0033-068X 10.1143/PTP.85.985
76. N. Yamada S. Takagi Prog. Theor. Phys. 86, 599 (1991); PTPKAV 0033-068X 10.1143/PTP.86.599
77. N. Yamada S. Takagi Prog. Theor. Phys. 87, 77 (1992); PTPKAV 0033-068X 10.1143/PTP.87.77
78. N. Yamada, Sci. Rep. Tohoku Univ., Ser. 8 SRTAD9 0388-5607 12, 177 (1992);
79. N. Yamada Phys. Rev. A 54, 182 (1996). PLRAAN 1050-2947 10.1103/PhysRevA.54.182
80. J.J. Halliwell and E. Zafiris, Phys. Rev. D PRVDAQ 0556-2821 57, 3351 (1998). 10.1103/PhysRevD.57.3351
81. J.B. Hartle, Phys. Rev. D PRVDAQ 0556-2821 44, 3173 (1991). 10.1103/PhysRevD.44.3173
82. J. Echanobe, A. del Campo, and J.G. Muga, Phys. Rev. A 77, 032112 (2008). PLRAAN 1050-2947 10.1103/PhysRevA.77.032112
83. J. Yearsley (unpublished).
84. A. Auerbach and S. Kivelson, Nucl. Phys. NUPBBO 0550-3213 B257, 799 (1985); 10.1016/0550-3213(85)90377-3
85. P. van Baal, in Lectures on Path Integration, edited by, H.A. Cerdeira, (World Scientific, Singapore, 1993);
86. also available from http://www.lorentz.leidenuniv.nl/vanbaal/HOME/publ. html.
87. J.J. Halliwell and M.E. Ortiz, Phys. Rev. D PRVDAQ 0556-2821 48, 748 (1993). 10.1103/PhysRevD.48.748
88. J.J. Halliwell, Phys. Lett. A 207, 237 (1995). PYLAAG 0375-9601 10.1016/0375-9601(95)00703-6
89. J.J. Halliwell, Phys. Rev. D PRVDAQ 0556-2821 64, 044008 (2001). 10.1103/PhysRevD.64.044008 (Pubitemid 33796144)
90. L.S. Schulman, Techniques and Applications of Path Integration (Wiley and Sons, New York, 1981), Chap.7.
91. N.F. Mott, Proc. R. Soc. A PRLAAZ 0080-4630 126, 79 (1929); 10.1098/rspa.1929.0205
92. reprinted in Quantum Theory and Measurement, edited by, J. Wheeler, and, W. Zurek, (Princeton University Press, Princeton, New Jersey, 1983);
93. For further discussions of the Mott calculation see also, J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, United Kingdom, 1987);
94. A.A. Broyles, Phys. Rev. A 48, 1055 (1993); PLRAAN 1050-2947 10.1103/PhysRevA.48.1055
95. M. Castagnino and R. Laura, Int. J. Theor. Phys. 39, 1737 (2000); IJTPBM 0020-7748 10.1023/A:1003681328934
96. J. Barbour, Classical Quantum Gravity CQGRDG 0264-9381 11, 2853 (1994); 10.1088/0264-9381/11/12/005
97. J. Barbour Classical Quantum Gravity CQGRDG 0264-9381 11, 2875 (1994). 10.1088/0264-9381/11/12/006
98. J.B. Hartle and S.W. Hawking, Phys. Rev. D PRVDAQ 0556-2821 28, 2960 (1983). 10.1103/PhysRevD.28.2960
99. J.J. Halliwell, Phys. Rev. D PRVDAQ 0556-2821 39, 2912 (1989); 10.1103/PhysRevD.39.2912
100. C. Kiefer, Classical Quantum Gravity CQGRDG 0264-9381 4, 1369 (1987); 10.1088/0264-9381/4/5/031
101. T. Padmanabhan, Phys. Rev. D PRVDAQ 0556-2821 39, 2924 (1989). 10.1103/PhysRevD.39.2924