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Decoherent Histories for Space–Time Domains

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Time in Quantum Mechanics

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References

  1. G.S. Agarwal: Phys. Rev. A3, 828 (1971); 4, 739 (1971); H. Dekker: Phys. Rev. A16, 2116 (1977); Phys. Rep. 80, 1 (1991); G.W. Ford, M. Kac, P. Mazur: J. Math. Phys. 6, 504 (1965); H. Grabert, P. Schramm, G.-L. Ingold: Phys. Rep. 168, 115 (1988); V. Hakim, V. Ambegaokar: Phys. Rev. 32, 423 (1985); J. Schwinger: J. Math. Phys. 2, 407 (1961); I.R. Senitzky: Phys. Rev. 119, 670 (1960)

    ADS  Google Scholar 

  2. G.R. Allcock: Ann. Phys. 53, 253 (1969); 53, 286 (1969);53, 311 (1969)

    Article  ADS  Google Scholar 

  3. Y. Aharanov, J. Oppenheim, S. Popescu, B. Reznik, W. Unruh: Phys. Rev. A 57, 4130 (1998); Phys.Rev. A 57, 4130 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  4. A. Auerbach, S. Kivelson: Nucl. Phys. B 257, 799 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  5. P. van Baal: ‘Tunneling and the path decomposition expansion’. In Lectures on Path Integration: Trieste 1991, ed. by H.A.Cerdeira et al. (World Scientific, Singapore, 1993)

    Google Scholar 

  6. N. Balazs, B.K. Jennings: Phys. Rep. 104, 347 (1984); M.Hillery, R.F. O’Connell, M.O. Scully, E.P. Wigner: Phys. Rep. 106, 121 (1984); V.I. Tatarskii: Sov. Phys. Usp 26, 311 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  7. J. Barbour: Class. Qu. Grav. 11, 2853 (1994); 11, 2875 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  8. M.A. Burschka, U.M. Titulaer: J. Stat. Phys. 25, 569 (1981); 26, 59 (1981); Physica A 112, 315 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  9. A. Boutet de Monvel, P. Dita: J. Phys. A 23, L895 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  10. A.O. Caldeira, A.J. Leggett: Physica A 121, 587 (1983)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. H. Carmichael: An Open Systems Approach to Quantum Optics (Springer-Verlag Lecture Notes in Physics, m18, Berlin, 1993)

    MATH  Google Scholar 

  12. H.S. Carslaw: Proc. Lond. Math. Soc. 30, 121 (1899)

    Google Scholar 

  13. H.F. Dowker, J.J. Halliwell: Phys. Rev. D 46, 1580 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  14. H. Fertig: Phys. Rev. Lett. 65, 2321 (1990)

    Google Scholar 

  15. R.P. Feynman, F.L. Vernon: Ann. Phys. 24, 118 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  16. C.W. Gardiner: Quantum Noise (Springer-Verlag, Berlin, 1991)

    MATH  Google Scholar 

  17. M. Gell-Mann, J.B. Hartle: Complexity, Entropy and the Physics of Information, SFI Studies in the Sciences of Complexity, Vol. VIII, ed. by W. Zurek (Addison-Wesley, Reading, 1990); in Proceedings of the Third International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, ed. by S. Kobayashi, H. Ezawa, Y. Murayama, S. Nomura (Physical Society of Japan, Tokyo, 1990)

    Google Scholar 

  18. M. Gell-Mann, J.B. Hartle: Phys. Rev. D 47, 3345 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  19. M. Gell-Mann, J.B. Hartle: Proceedings of the 4th Drexel Symposium on Quantum Non-Integrability – The Quantum-Classical Correspondence, ed. by D.H. Feng, B.L. Hu (International Press, Boston/Hong Kong, 1996)

    Google Scholar 

  20. R.B. Griffiths: J. Stat. Phys. 36, 219 (1984); Phys. Rev. Lett. 70, 2201 (1993); Am. J. Phys. 55, 11 (1987)

    Article  MATH  ADS  Google Scholar 

  21. N. Grot, C. Rovelli, R.S. Tate: Phys. Rev. A 54, 4676 (1996); Phys. Rev. A 54, 4679 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  22. J.J. Halliwell: ‘Aspects of the decoherent histories approach to quantum theory’. In: Stochastic Evolution of Quantum States in Open Systems and Measurement Processes, ed. by L. Di’osi, B. Luk’acs (World Scientific, Singapore, 1994)

    Google Scholar 

  23. J.J. Halliwell: ‘A review of the decoherent histories approach to quantum mechanics’. In Fundamental Problems in Quantum Theory, ed. by D.Greenberger, A. Zeilinger, Annals of the New York Academy of Sciences, Vol. 775, 726 (1994).

    Google Scholar 

  24. J.J. Halliwell: Phys. Lett. A 207, 237 (1995)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  25. J.J. Halliwell: General Relativity and Gravitation 1992, ed. by R.J. Gleiser, C.N. Kozameh, O.M. Moreschi (IOP Publishers, Bristol, 1993)

    Google Scholar 

  26. J.J. Halliwell: Phys. Rev. D 60, 105031 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  27. J.J. Halliwell: Prog. Th. Phys. 102, 707 (1999)

    Article  ADS  Google Scholar 

  28. J.J. Halliwell: Phys.Rev. D 64, 044008 (2001)

    Google Scholar 

  29. J.J. Halliwell, M.E. Ortiz: Phys. Rev. D 48, 748 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  30. J.J. Halliwell, J. Thorwart: Phys. Rev. D 64, 124018 (2001)

    Google Scholar 

  31. J.J. Halliwell, A. Zoupas: Phys. Rev. D 52, 7294 (1995) Phys. Rev. D 55, 4697 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  32. J.J. Halliwell, E. Zafiris: Phys. Rev. D 57, 3351 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  33. J.J. Halliwell, J. Thorwart: Phys. Rev. D 65, 104009 (2002)

    Google Scholar 

  34. J.J. Halliwell, P. Wallden: Phys. Rev. D 73, 024011 (2006)

    Google Scholar 

  35. J.B. Hartle: Phys. Rev. D 44, 3173 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  36. J.B. Hartle: Phys. Rev. D 38, 2985 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  37. J.B. Hartle: Quantum Cosmology and Baby Universes, ed. by S. Coleman, J. Hartle, T. Piran, S. Weinberg (World Scientific, Singapore, 1991)

    Google Scholar 

  38. J.B. Hartle: Phys. Rev. D 37, 2818 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  39. J.B. Hartle: Proceedings of the 1992 Les Houches Summer School, Gravitation et Quantifications, ed. by B. Julia, J. Zinn-Justin (Elsevier Science B.V., Amsterdams 1995)

    Google Scholar 

  40. E.H. Hauge, J.A. Stovneng: Rev. Mod. Phys. 61, 917 (1989)

    Article  ADS  Google Scholar 

  41. A.S. Holevo: Probabilistic and Statistical Aspects of Quantum Theory (North-Holland Publishing Corporation, Amsterdam, 1982)

    MATH  Google Scholar 

  42. C. Isham: J. Math. Phys. 23, 2157 (1994); C. Isham, N. Linden: J. Math. Phys. 35, 5452 (1994); 36, 5392 (1995); C. Isham, N. Linden, S. Schreckenberg: J. Math. Phys. 35, 6360 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  43. A. Jadcyk: Prog. Theor. Phys. 93, 631 (1995); Ph. Blanchard, A. Jadczyk: Helv. Phys. Acta. 69, 613 (1996)

    Article  ADS  Google Scholar 

  44. That the propagator for the Fokker–Planck equation can be represented in terms of a configuration space path integral of this form does not appear to be widely known. See, however, H. Kleinert: Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (World Scientific, Singapore, 1990)

    Google Scholar 

  45. J. Kijowski: Rep. Math. Phys. 6, 362 (1974)

    MathSciNet  ADS  Google Scholar 

  46. D.H. Kobe, V.C. Aguilera-Navarro: Phys. Rev. A50, 933 (1994)

    ADS  MathSciNet  Google Scholar 

  47. N. Kumar: Pramana J. Phys. 25, 363 (1985)

    Article  ADS  Google Scholar 

  48. R. Landauer: Rev. Mod. Phys. 66, 217 (1994); Ber. Bunsenges: Phys. Chem 95, 404 (1991)

    Article  ADS  Google Scholar 

  49. G. Lindblad: Commun. Math. Phys. 48, 119 (1976)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  50. L. Mandelstamm, I. Tamm: J. Phys. 9, 249 (1945)

    Google Scholar 

  51. T.W. Marshall, E.J. Watson: J. Phys. A 18, 3531 (1985); J. Phys. A 20, 1345 (1987)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. R.J. Micanek, J.B. Hartle: Phys. Rev. A 54, 3795 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  53. N.F. Mott: Proc. R. Soc A 124, 375 (1929)

    Article  ADS  Google Scholar 

  54. J.G. Muga, A.D. Baute, J.A. Damborenea, I.L. Egusquiza: quant-ph/0009111 (2000)

    Google Scholar 

  55. J.G. Muga, S. Brouard, D. Mac’ias: Ann. Phys. (N.Y.) 240, 351 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  56. J.G. Muga, C.R. Leavens: Phys. Rep. 338, 353 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  57. R. Omnés: J. Stat. Phys. 53, 893 (1988); 53, 933 (1988); 53, 957 (1988); 57, 357 (1989); 62, 841 (1991); Ann. Phys. 201, 354 (1990); Rev. Mod. Phys. 64, 339 (1992); The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1994)

    Article  MATH  ADS  Google Scholar 

  58. J.P. Palao, J.G. Muga, S. Brouard, A. Jadczyk: Phys. Lett. A233, 227 (1997)

    Google Scholar 

  59. A. Peres: Quantum Theory: Concepts and Methods (Kluwer Academic Publishers, Dordrecht, 1993)

    MATH  Google Scholar 

  60. L.S. Schulman: Time’s Arrows and Quantum Measurement (Cambridge University Press, Cambridge, 1997)

    Google Scholar 

  61. L.S. Schulman: Ann. Phys. 212, 315 (1991); B. Gaveau, L.S. Schulman: J. Stat. Phys. 58, 1209 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  62. L. Schulman, R.W. Ziolkowiski: in Path integrals from meV to MeV, ed. by V. Sa-yakanit, W. Sritrakool, J. Berananda, M.C. Gutzwiller, A. Inomata, S. Lundqvist, J.R. Klauder, L.S. Schulman (World Scientific, Singapore, 1989)

    Google Scholar 

  63. A.J.F. Siegert: Phys. Rev. 81, 617 (1951)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  64. See, for example, E.P. Wigner: Phys. Rev. 98, 145 (1955); F.T. Smith: Phys. Rev. 118, 349 (1960); E. Gurjoy, D. Coon: Superlattices Microsctruct. 5, 305 (1989); C. Piron: in Interpretation and Foundations of Quantum Theory, ed. by H. Newmann (Bibliographisches Institute, Mannheim, 1979)

    Google Scholar 

  65. M.C. Wang, G.E. Uhlenbeck: Rev. Mod. Phys. 17, 323 (1945); reprinted in, Selected Papers on Noise and Stochastic Processes, ed. by N. Wax (Dover Publications, New York, 1954)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  66. P. Wallden: gr-qc/0607072.

    Google Scholar 

  67. N. Yamada: Phys. Rev. 54, 182 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  68. N. Yamada, S. Takagi: Prog. Theor. Phys. 85, 985 (1991); 86, 599 (1991); 87, 77 (1992); N. Yamada: Sci. Rep. T^ohoku Univ. Ser. 8 12, 177 (1992)

    Google Scholar 

  69. E. Zafiris: Imperial College preprint TP/96-97/05 (1997)

    Google Scholar 

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Halliwell, J.J. (2008). Decoherent Histories for Space–Time Domains. In: Muga, J., Mayato, R.S., Egusquiza, Í. (eds) Time in Quantum Mechanics. Lecture Notes in Physics, vol 734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73473-4_6

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