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Foundations of Quantum Mechanics: A Quantum Probabilistic Approach

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The Nature of Quantum Paradoxes

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 28))

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Bibliography

  1. Accardi, L. : 1974, “Non-commutative Markov chains,” in Proceedings School of Mathematical Physics, Universitd di Camerino, Sept-Oct. 1974.

    Google Scholar 

  2. Accardi, L. : “On the noncommutative Markov property,” Funct. Anal. Appl. 9 (1975) 1.

    Article  MATH  MathSciNet  Google Scholar 

  3. Accardi, L. : “Nonrelativistic Quantum Mechanics as a noncommutative Markov process,” Adv. Math. 20 (1976) 329–366.

    Article  MATH  MathSciNet  Google Scholar 

  4. Accardi, L.: “Noncommutative Markov chains associated to a preassigned evolution. An application to the quantum theory of measurement,” Adv. Math. 29 (1976) 329–366.

    Article  MathSciNet  Google Scholar 

  5. Accardi, L.: “On the quantum Feynman-Kac formula,” Rend. Sem. Mat. Fis. Univ. 1. Polit. Milano ,48(1978) 135–179.

    Article  MATH  MathSciNet  Google Scholar 

  6. Accardi, L.: “Topics in quantum probability,” Phys. Rep. 77 (1981) 169–192.

    Article  ADS  MathSciNet  Google Scholar 

  7. Accardi, L.: “Probabilita e teoria quantistica,”Physis 23 (1981) 485–524.

    MATH  MathSciNet  Google Scholar 

  8. Accardi, L.: “Stato fisico,”Enciclopedia Einaudi Vol.XIII (1981) 514–548.

    Google Scholar 

  9. Accardi, L.: “Foundations of quantum Probability,”in Rend. Sent. Mat. Univ. Polit. Torino (1982)245–273.

    Google Scholar 

  10. Accardi, L., and C. Cecchini: “Conditional expecations in von Neumann algebras and a theorem of Takesaki,”J. Funct. Anal. 45 (1982) 245–273.

    Article  MATH  MathSciNet  Google Scholar 

  11. Accardi, L., and A. Fedullo: “On the statistical meaning of complex numbers in quantum theory,”ett.Nuovo Cim

    Google Scholar 

  12. Accardi, L., and A. Frigerio: “Markovian cocycles,”Proc. Royal Irish Acad. 83A (1983)251–263.

    MathSciNet  Google Scholar 

  13. Accardi, L., Frigerio, A., and J. Lewis: “Quantum stochastic processes,”Pub. R.I.MS. Kyoto 18 (1982) 37–133.

    MathSciNet  Google Scholar 

  14. Accardi, L. : “The probabilistic roots of the quantum mechanical paradoxes,”in The Wave Particle Dualism ,S. Diner, G. Lochak, and F. Selleri (eds.), Reidel, Dordrecht, 1983.

    Google Scholar 

  15. Accardi, L. : “Probabilita’ classica,”in Dizionario delle Scienze Fisiche. Istituto dell Enciclopedia Italiana ,Rome, 1983.

    Google Scholar 

  16. Accardi, L.: “Some trends and problems in quantum probability,”in Quantum Pro-bability And Applications to the Quantum Theory of Irreversible Processes Springer LNM 1055, 1–19.

    Google Scholar 

  17. Accardi, L., and A. Bach: “Quantum central limit theorems for strongly mixing random variables,”Z. Wahrsch. Verw. Geb. 68 (1985) 393–402.

    Article  MATH  MathSciNet  Google Scholar 

  18. Accardi, L. : “Quantum stochastic processes,”in Statistical Physics and dynamical systems: Rigorous Results ,Second Colloquim, Birkheuser, Boston, 1985.

    Google Scholar 

  19. Accardi, L. : “Non-Kolmogorovian probabilistic models and quantum theory,”invited talk at the 45th ISI Conference, Amsterdam, August 1985, to appear.

    Google Scholar 

  20. Accardi, L.: “On the universality of the Einstein-Podolsky-Rosen phenomenon,”to appear.

    Google Scholar 

  21. Aerts, D. : “A possible explanation for the probabilities of quantum mechanics,”J. Math. Phys. to appear 1985.

    Google Scholar 

  22. Aspect, A., G. Dalibard, and G. Roger: “Experimental test of Bell’s inequalities using time-varying analyzers,”Phys. Rev. Lett. 49 (1982) 1804–1807.

    Article  ADS  MathSciNet  Google Scholar 

  23. Barchielli, A., L. Lanz, and G. M. Prosperi: “A model for the macroscopic description of continual observables in quantum mechanics,”Nuovo Cim. 72B (1982) 69.

    ADS  MathSciNet  Google Scholar 

  24. Barchielli, A., and G. Lupieri: in Quantum Probability and Applications II ,Springer LNM 1136 (1985) 57–66.

    Chapter  Google Scholar 

  25. Bell, J. S. : “On the problem of hidden variables in quantum mechanics,”Rev. Mod. Phys. 38 (1966) 447–452.

    Article  ADS  MATH  Google Scholar 

  26. Bell, J. S.: “The theory of local beables,”Epist. Lett. (1975).

    Google Scholar 

  27. Bell, J. S.: “Bertlmann’ s socks and the nature of reality,”J. de Physique Colloque C 2, Suppl. N3, 42 (1981) 41–62. Epist. Lett. (1976).

    Google Scholar 

  28. Beltrametti, E., and G. Cassinelli: The Logic of Quantum Mechanics ,Addison-Wesley, New York, 1982.

    Google Scholar 

  29. Bergia S., F. Cannata, S. Russo, and M. Savoia: “Group theoretical interpretation of von Neumann’ s theorem on composite systems. Am. J. Phys. 47 (1979) 548–552.

    Article  ADS  Google Scholar 

  30. Chentzov, N. N., and E A. Morozova: “Noncommutative quantum logics,”(in Russian), Inst. Appl. Math. Keldish preprint No. 57 (1981).

    Google Scholar 

  31. Chentzov, N. N., and E. A. Morozova: “Probability distributions on noncommutative logics (finite dimensional theory),”(in Russian), Inst. Appl. Math. Keldish pre-print No. 129 (1981).

    Google Scholar 

  32. Cook R., M. Keane, and W. Moran: “An elementary proof of Gleason’ s theorem,”Math. Proc. Camb. Phil. Soc. 98 (1985) 117–128.

    Article  Google Scholar 

  33. Daneri, A., A. Loinger, and G. M. Prosperi: “Quantum theory of measurement and the ergodicity conditions,”Nucl. Phys. 33 (1962) 297–319.

    Article  MATH  MathSciNet  Google Scholar 

  34. Davies, E. B. : “Quantum Theory of Open Systems,”Academic Press, New York, 1976.

    MATH  Google Scholar 

  35. Davies, E. B., and J. T. Lewis: “An operational approach to quantum probability,”Comm. Math. Phys. 17 (3) (1970) 239–260.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  36. Feynmann, R. P. : “The concept of probability in quantum mechanics,”in Proc.2nd Berkeley Symp. Math. Stat. Prob.; University of California Press, Berkeley,(1951)533–541.

    Google Scholar 

  37. Feynmann, R. P. : “Space-time approach to non-relativistic quantum mechanics,”Rev. of Mod. Phys. 20 (1948) 367–385.

    Article  ADS  Google Scholar 

  38. Feynmann, R. P. : The Nature of Physical Law ,(Italian edn.) Boringhieri, Torino,Italy, 1971.

    Google Scholar 

  39. Frigerio, A., and V. Gorini: Dynamics of Nonrelativistic Quantum Systems ,to appear in Series Encyclopedia of Mathematics and its Applications.

    Google Scholar 

  40. Garuccio, A., and D. Gutkowski: “Comparison between local Kolmogorovian models and Bell’s inequality,”preprint, 1985.

    Google Scholar 

  41. Gleason, A. M. : “Measures on closed subspaces of Hilbert space,”J.Math.Mech.6 (1957) 885–893.

    MATH  MathSciNet  Google Scholar 

  42. Gudder, S., and N. Zanghi: “Probability models,”Nuovo Cim. B 79 (1984) 291.

    Article  ADS  MathSciNet  Google Scholar 

  43. Guerra, F. : “Structural aspects of stochastic mechanics and stochastic field theory,”Phys. Rep. 77 (1981).

    Google Scholar 

  44. Helstrom, C. W.: Statistical Theory of Signal Detection ,Pergamon Press, 1968, 2nd edn.

    Google Scholar 

  45. Holevo, A. : Probabilistic and Statistical Aspects of Quantum Theory ,North Holland, Amsterdam, 1982.

    MATH  Google Scholar 

  46. Holevo, A. : Statistical Structure of Quantum Mechanics and Hidden Parameters ,(in Russian) Znanie, Mosow, 1985.

    Google Scholar 

  47. Hudson, R., and K. R. Parthasarathy: “Quantum Ito’ s formula and stochastic evolutions,” Comm Math. Phys. 93 (1984) 301–323.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  48. Jammer, M.: The Philosophy of Quantum Mechanics ,Wiley, New York, 1974.

    Google Scholar 

  49. Kochen, S., and E. P. Specker. “The problems of hidden variables in quantum mechanics,” J. Math. Mech. 17 (1967) 59–67.

    MATH  MathSciNet  Google Scholar 

  50. Kraus, K.: States, Effects and Operations ,Springer, LNP 190,1983.

    Google Scholar 

  51. Kruszinsky, P. : “Extensions of Gleason’s,” in Quantum probability and applications ,Springer LNM 1055, 1984. 1984. 1984. 1984. 1984. 1984. 1984. 1984. 1984. 1984. 1984. 1984. 1984. 1984. 1984. 1984.1984.1984.1984.

    Google Scholar 

  52. Lindblad, G. : “Entropy, information and quantum measurement,” Comm. Math. Phys. 33 (1973) 305–322.

    Article  ADS  MathSciNet  Google Scholar 

  53. Ludwig, G.: Foundations of quantum mechanics ,Springer, New York, 1983.

    MATH  Google Scholar 

  54. Mackey, G. W. : Mathematical Foundations of Quantum Mechanics ,Addison-Wesley, New York, 1976.

    Google Scholar 

  55. Margenau, H., and J. L. Park: “The logic of noncommutability of quantum mechanical operators and its empirical conseqences,” in Perspectives in Quantum Theory, W. Yourgrau and A. van der Merwe (eds.), Dover, New York, 1971.

    Google Scholar 

  56. Nelson, E. : Dynamical Theories of Brownian motion ,Princeton University Press, Princeton, NJ, 1967.

    MATH  Google Scholar 

  57. Nelson, E.: Quantum fluctuations. Princeton University Press, Princeton, NJ, 1985.

    MATH  Google Scholar 

  58. Nelson, E : “The locality problem in stochastic mechanics,” Presented to the Conference on New Techniques and Ideas in Quantum Measurement theory, New York Academy of Sciences, New York, January, 1986.

    Google Scholar 

  59. Ozawa, M. : “Quantum measuring process of continuous observables,” Journ. of Math. Phys. 25 (1985) 79–87.

    Article  ADS  Google Scholar 

  60. Pashkievicz, A. : “Measures on projections of von Neumann algebras,” J. Funct. Anal. 62 (1985) 87–117.

    Article  MathSciNet  Google Scholar 

  61. Piron , C.: Foundations of Quantum Physics ,Addison-Wesley, New York, 1976.

    MATH  Google Scholar 

  62. Popper, K.: “Realism in quantum mechanics and a new version of the EPR experiment” in Open questions in Quantum Physics, G.Tarozzi, A. van der Merwe (eds.) Reidel, Dordrecht, 1985.

    Google Scholar 

  63. Prosperi, G. M. : “Macroscopic physics and the problem of measurement in quantum mechanics,” in Foundations of Quantum Mechanics ,Varenna IL Corso 1971 Academic Press, New York.

    Google Scholar 

  64. Rauch, H. : “Tests of quantum mechanics by neutron interferometry,” in Open Questions in Quantum Physics ,G. Tarozzi, A. van der Merwe (eds.) Reidel, Dordrecht, 1985.

    Google Scholar 

  65. Santos, E.: “The wave particle dualism,” (review) Found. of Phys. 15 (1985) 229–231.

    Article  ADS  Google Scholar 

  66. Sakai, S.: C* -Algebras and W*-Algebras ,Springer, New York, 1971.

    Google Scholar 

  67. Schwinger, J. : Quantum Kinematics and Dynamics ,Academic Press, New York, 1970.

    MATH  Google Scholar 

  68. Srinivas, M. D. : “Collapse postulate for observables with continuous spectrum,” Comm. Math. Phys. 71 (1980) 131–158.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  69. Stormer, E. : “On projection maps of von Neumann algebras,” Math. Scand. 30 (1972)46–50.

    MathSciNet  Google Scholar 

  70. Vogt, A. : “Position and momentum distributions do not determine the quantum mechanical state,” in Mathematical Foundations of Quantum Theory, A. R. Marlow (ed.), Academic Press, New York, 1978.

    Google Scholar 

  71. von Neumann, J. : Mathematical Foundations of Quantum Mechanics ,Princeton University Press, Princeton, NJ, 1955.

    MATH  Google Scholar 

  72. Wightman, A. S.: “Hilberf’ s sixth problem: mathematical treatment of the axioms of physics,” in Mathematical Developements Arising from Hilbert Problems, Proa Symp. in Pure Math. 28 ,(1976) AMS, Providence, 1976.

    Google Scholar 

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Accardi, L. (1988). Foundations of Quantum Mechanics: A Quantum Probabilistic Approach. In: Tarozzi, G., van der Merwe, A. (eds) The Nature of Quantum Paradoxes. Fundamental Theories of Physics, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2947-0_14

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  • DOI: https://doi.org/10.1007/978-94-009-2947-0_14

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