An effective stochastic semiclassical theory for the gravitational field

International Journal of Theoretical Physics

Volumn 38, Issue 11, 1999, Pages 3049-3089

  Martin, Rosario ^a   Verdaguer, Enric ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033228934     PISSN: 00207748     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026668418065     Document Type: Article

References (73)

1. [1] L. H. Ford, Ann. Phys. 144, 238 (1982).
2. [2] C.-I. Kuo and L. H. Ford, Phys. Rev. D 47, 4510 (1993); N. G. Phillips and B.-L. Hu, Phys. Rev. D 55, 6123 (1997).
3. [2] C.-I. Kuo and L. H. Ford, Phys. Rev. D 47, 4510 (1993); N. G. Phillips and B.-L. Hu, Phys. Rev. D 55, 6123 (1997).
4. [3] B.-L. Hu, Physica A 158, 399 (1989).
5. [4] R. P. Feynman and F. L. Vernon, Ann. Phys. 24, 118 (1963).
6. [5] R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
7. [6] E. Calzetta and B.-L. Hu, Phys. Rev. D 49, 6636 (1994).
8. [7] B.-L. Hu and A. Matacz, Phys. Rev. D 51, 1577 (1995).
9. [8] B.-L. Hu and S. Sinha, Phys. Rev. D 51, 1587 (1995).
10. [9] A. O. Caldeira and A. J. Legget, Physica A 121, 587 (1983).
11. [10] B.-L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992).
12. [11] B.-L. Hu and A. Matacz, Phys. Rev. D 49, 6612 (1994).
13. [12] C. Greiner and B. Müller, Phys. Rev. D 55, 1026 (1997).
14. [13] A. Campos and E. Verdaguer, Phys. Rev. D 53, 1927 (1996).
15. [14] F. C. Lombardo and F. D. Mazzitelli, Phys. Rev. D 55, 3889 (1997).
16. [15] A. Campos and E. Verdaguer, Int. J. Theor. Phys. 36, 2525 (1997); E. Calzetta, A. Campos, and E. Verdaguer, Phys. Rev. D 56, 2163 (1997).
17. [15] A. Campos and E. Verdaguer, Int. J. Theor. Phys. 36, 2525 (1997); E. Calzetta, A. Campos, and E. Verdaguer, Phys. Rev. D 56, 2163 (1997).
18. [16] A. Campos and B.-L. Hu, Phys. Rev. D 58, 125021 (1998).
19. [17] B.-L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 47, 1576 (1993).
20. [18] A. Matacz, Phys. Rev. D 55, 1860 (1997).
21. [19] M. Morikawa, Phys. Rev. D 33, 3607 (1986); D.-S. Lee and D. Boyanovsky, Nucl. Phys. B 406, 631 (1993).
22. [19] M. Morikawa, Phys. Rev. D 33, 3607 (1986); D.-S. Lee and D. Boyanovsky, Nucl. Phys. B 406, 631 (1993).
23. [20] R. Zh. Shaisultanov, hep-th/9509154; hep-th/9512144.
24. [21] M. Gleiser and R. O. Ramos, Phys. Rev. D 50, 2441 (1994); D. Boyanovsky, H. J. de Vega, R. Holman, D. S. Lee, and A. Singh, Phys. Rev. D 51, 4419 (1995); E. Calzetta and B.-L. Hu, Phys. Rev. D 55, 3536 (1997); M. Yamaguchi and J. Yokoyama, Phys. Rev. D 56, 4544 (1997); S. A. Ramsey, B.-L. Hu, and A. M. Stylianopoulos, Phys. Rev. D 57, 6003 (1998).
25. [21] M. Gleiser and R. O. Ramos, Phys. Rev. D 50, 2441 (1994); D. Boyanovsky, H. J. de Vega, R. Holman, D. S. Lee, and A. Singh, Phys. Rev. D 51, 4419 (1995); E. Calzetta and B.-L. Hu, Phys. Rev. D 55, 3536 (1997); M. Yamaguchi and J. Yokoyama, Phys. Rev. D 56, 4544 (1997); S. A. Ramsey, B.-L. Hu, and A. M. Stylianopoulos, Phys. Rev. D 57, 6003 (1998).
26. [21] M. Gleiser and R. O. Ramos, Phys. Rev. D 50, 2441 (1994); D. Boyanovsky, H. J. de Vega, R. Holman, D. S. Lee, and A. Singh, Phys. Rev. D 51, 4419 (1995); E. Calzetta and B.-L. Hu, Phys. Rev. D 55, 3536 (1997); M. Yamaguchi and J. Yokoyama, Phys. Rev. D 56, 4544 (1997); S. A. Ramsey, B.-L. Hu, and A. M. Stylianopoulos, Phys. Rev. D 57, 6003 (1998).
27. [21] M. Gleiser and R. O. Ramos, Phys. Rev. D 50, 2441 (1994); D. Boyanovsky, H. J. de Vega, R. Holman, D. S. Lee, and A. Singh, Phys. Rev. D 51, 4419 (1995); E. Calzetta and B.-L. Hu, Phys. Rev. D 55, 3536 (1997); M. Yamaguchi and J. Yokoyama, Phys. Rev. D 56, 4544 (1997); S. A. Ramsey, B.-L. Hu, and A. M. Stylianopoulos, Phys. Rev. D 57, 6003 (1998).
28. [21] M. Gleiser and R. O. Ramos, Phys. Rev. D 50, 2441 (1994); D. Boyanovsky, H. J. de Vega, R. Holman, D. S. Lee, and A. Singh, Phys. Rev. D 51, 4419 (1995); E. Calzetta and B.-L. Hu, Phys. Rev. D 55, 3536 (1997); M. Yamaguchi and J. Yokoyama, Phys. Rev. D 56, 4544 (1997); S. A. Ramsey, B.-L. Hu, and A. M. Stylianopoulos, Phys. Rev. D 57, 6003 (1998).
29. [22] J. Schwinger, J. Math. Phys. 2, 407 (1961); Phys. Rev. 128, 2425 (1962); P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 4, 1 (1963); 4, 12 (1963); L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]; J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, Massachusetts, 1970).
30. [22] J. Schwinger, J. Math. Phys. 2, 407 (1961); Phys. Rev. 128, 2425 (1962); P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 4, 1 (1963); 4, 12 (1963); L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]; J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, Massachusetts, 1970).
31. [22] J. Schwinger, J. Math. Phys. 2, 407 (1961); Phys. Rev. 128, 2425 (1962); P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 4, 1 (1963); 4, 12 (1963); L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]; J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, Massachusetts, 1970).
32. [22] J. Schwinger, J. Math. Phys. 2, 407 (1961); Phys. Rev. 128, 2425 (1962); P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 4, 1 (1963); 4, 12 (1963); L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]; J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, Massachusetts, 1970).
33. [22] J. Schwinger, J. Math. Phys. 2, 407 (1961); Phys. Rev. 128, 2425 (1962); P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 4, 1 (1963); 4, 12 (1963); L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]; J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, Massachusetts, 1970).
34. [22] J. Schwinger, J. Math. Phys. 2, 407 (1961); Phys. Rev. 128, 2425 (1962); P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 4, 1 (1963); 4, 12 (1963); L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]; J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, Massachusetts, 1970).
35. [22] J. Schwinger, J. Math. Phys. 2, 407 (1961); Phys. Rev. 128, 2425 (1962); P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 4, 1 (1963); 4, 12 (1963); L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]; J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, Massachusetts, 1970).
36. [23] K.-C. Chou, Z.-B. Su, B.-L. Hao, and L. Yu, Phys. Rep. 118, 1 (1985); N. P. Landsman and Ch. G. van Weert, Phys. Rep. 145, 141 (1987).
37. [23] K.-C. Chou, Z.-B. Su, B.-L. Hao, and L. Yu, Phys. Rep. 118, 1 (1985); N. P. Landsman and Ch. G. van Weert, Phys. Rep. 145, 141 (1987).
38. [24] R. B. Griffiths, J. Stat. Phys. 36, 219 (1984).
39. [25] R. Omnès, Rev. Mod. Phys. 64, 339 (1992), and references therein; R. Omnès, The Interpretation of Quantum Mechanics Princeton University Press, Princeton, New Jersey, 1994).
40. [25] R. Omnès, Rev. Mod. Phys. 64, 339 (1992), and references therein; R. Omnès, The Interpretation of Quantum Mechanics Princeton University Press, Princeton, New Jersey, 1994).
41. [26] M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47, 3345 (1993).
42. [27] J. B. Hartle, In Gravitation and Quantizations, B. Julia and J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1995), and references therein; gr-qc/9304006.
43. [28] J. J. Halliwell, In Stochastic Evolution of Quantum States in Open Systems and Measurement Processes, L. Diósi, ed. (World Scientific, Singapore, 1994), gr-qc/9308005.
44. [29] J. J. Halliwell, Ann N. Y. Acad. Sci. 755, 726 (1995), and references therein.
45. [30] J. P. Paz and W. H. Zurek, Phys. Rev. D 48, 2728 (1993).
46. [31] H. F. Dowker and J. J. Halliwell, Phys. Rev. D 46, 1580 (1992).
47. [32] J. J. Halliwell, Phys. Rev. D 48, 4785 (1993); 57, 2337 (1998).
48. [32] J. J. Halliwell, Phys. Rev. D 48, 4785 (1993); 57, 2337 (1998).
49. [33] R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
50. [34] E. S. Abers and B. W. Lee, Phys. Rep. 9C, 1 (1973).
51. [35] S. Weinberg, The Quantum Theory of Fields, Vols. I and II (Cambridge University Press, Cambridge, 1995, 1996).
52. [36] V. Hakim and V. Ambegaokar, Phys. Rev. A 32, 423 (1985); C. Morais Smith and A. O. Caldeira, Phys. Rev. A 36, 3509 (1987).
53. [36] V. Hakim and V. Ambegaokar, Phys. Rev. A 32, 423 (1985); C. Morais Smith and A. O. Caldeira, Phys. Rev. A 36, 3509 (1987).
54. [37] H. Grabert, P. Schramm, and G.-L. Ingold, Phys. Rep. 168, 115 (1988).
55. [38] Z.-B. Su, L.-Y. Chen, X.-T. Yu, and K.-C. Chou, Phys. Rev. B 37, 9810 (1988).
56. [39] W. H. Zurek, In Conceptual Problems of Quantum Gravity, A. Ashtekar and J. Stachel, eds. (Birkhäuser, Boston, 1991); Phys. Today 44(10), 36 (1991); Vistas Astron. 37, 185 (1993).
57. [39] W. H. Zurek, In Conceptual Problems of Quantum Gravity, A. Ashtekar and J. Stachel, eds. (Birkhäuser, Boston, 1991); Phys. Today 44(10), 36 (1991); Vistas Astron. 37, 185 (1993).
58. [39] W. H. Zurek, In Conceptual Problems of Quantum Gravity, A. Ashtekar and J. Stachel, eds. (Birkhäuser, Boston, 1991); Phys. Today 44(10), 36 (1991); Vistas Astron. 37, 185 (1993).
59. [40] T. Brun, Phys. Rev. D 47, 3383 (1993); J. P. Paz, S. Habib, and W. H. Zurek, Phys. Rev. D 47, 488 (1993).
60. [40] T. Brun, Phys. Rev. D 47, 3383 (1993); J. P. Paz, S. Habib, and W. H. Zurek, Phys. Rev. D 47, 488 (1993).
61. [41] F. Lombardo and F. D. Mazzitelli, Phys. Rev. D 53, 2001 (1996); T. Tanaka and M. Sakagami, Prog. Theor. Phys. 100, 547 (1998).
62. [41] F. Lombardo and F. D. Mazzitelli, Phys. Rev. D 53, 2001 (1996); T. Tanaka and M. Sakagami, Prog. Theor. Phys. 100, 547 (1998).
63. [42] J. T. Whelan, Phys. Rev. D 57, 768 (1998); qr-qc/9702003.
64. [43] E. Joos and H. D. Zeh, Z. Phys. B 59, 223 (1985).
65. [44] E. Wigner, Phys. Rev. 40, 749 (1932); M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984); J. J. Halliwell, Phys. Rev. D 36, 3626 (1987).
66. [44] E. Wigner, Phys. Rev. 40, 749 (1932); M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984); J. J. Halliwell, Phys. Rev. D 36, 3626 (1987).
67. [44] E. Wigner, Phys. Rev. 40, 749 (1932); M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984); J. J. Halliwell, Phys. Rev. D 36, 3626 (1987).
68. [45] J. F. Donoghue, Phys. Rev. Lett. 72, 2996 (1994); Phys. Rev. D 50, 3874 (1994); Helv. Phys. Acta 69, 269 (1996); in Advanced School on Effective Theories, F. Cornet and M. J. Herrero, eds. (World Scientific, Singapore, 1996), gr-qc/9512024; gr-qc/9712070.
69. [45] J. F. Donoghue, Phys. Rev. Lett. 72, 2996 (1994); Phys. Rev. D 50, 3874 (1994); Helv. Phys. Acta 69, 269 (1996); in Advanced School on Effective Theories, F. Cornet and M. J. Herrero, eds. (World Scientific, Singapore, 1996), gr-qc/9512024; gr-qc/9712070.
70. [45] J. F. Donoghue, Phys. Rev. Lett. 72, 2996 (1994); Phys. Rev. D 50, 3874 (1994); Helv. Phys. Acta 69, 269 (1996); in Advanced School on Effective Theories, F. Cornet and M. J. Herrero, eds. (World Scientific, Singapore, 1996), gr-qc/9512024; gr-qc/9712070.
71. [45] J. F. Donoghue, Phys. Rev. Lett. 72, 2996 (1994); Phys. Rev. D 50, 3874 (1994); Helv. Phys. Acta 69, 269 (1996); in Advanced School on Effective Theories, F. Cornet and M. J. Herrero, eds. (World Scientific, Singapore, 1996), gr-qc/9512024; gr-qc/9712070.
72. [46] T. S. Bunch, J. Phys. A 12, 517 (1979).
73. [47] R. Martín and E. Verdaguer, gr-qc/9811070; Phys. Rev. D 60, 084008 (1999).