Stochastic-Dynamical Approach to Quantum Mechanics

  • Mikio Namiki
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 24)


We mainly discuss the Parisi-Wu stochastic quantization as a possible stochastic-dynamical approach to quantum mechanics, which gives quantum mechanics by thermal equilibrium limit of a hypothetical stochastic process in a new time other than the ordinary time. First we sketch its historical background in which one of the central problems is how to replace or reformulate quantum mechanics with a classical sto-chastic dynamics. After a brief survey of technical merits of the method, we examine a possibility of formulating the stochastic quantization in the Minkowski space-time, and speculate possible roots of the hypothetical stochastic process in the new time.


Wigner Function Langevin Equation Quantum Fluctuation Ordinary Time Husimi Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    For example, see; E. Schrödinger, 1931, Sitzungsb. Preuss. Akad. W. 144; Metadier, J., 1931, Comptes Rendus, 193, 1173; Furth, R., 1933, Zeits. f. Phys. 81, 143.Google Scholar
  2. [2]
    von Neumann, J. 1932, Mathematische Grundlagen der Quanten Mechanik (Springer, Berlin).Google Scholar
  3. [3]
    Bohm, D., 1952, Phys. Rev. 85 166.CrossRefADSMathSciNetGoogle Scholar
  4. [4]
    Vigier, J. P. and Roy, S., 1985, Hadronic J. Suppl., 1, 475.Google Scholar
  5. 5.
    For example, see; Takabayashi, T., 1984, Proc. of the International Symposium on Foundations of Quantum Mechanics (Phys. Soc. Japan, Tokyo), eds. S. Kamefuchi et al, p. 44.Google Scholar
  6. [6]
    Nelson, E., 1966, Phys. Rev., 150, 107.CrossRefGoogle Scholar
  7. [7]
    Parisi, G., and Wu, Yong-Shi, 1981, Sci. Sin., 24 483.Google Scholar
  8. [7.A]
    Klauder, J. R., 1983, Acta Phys. Austrica, Suppl. XXV (Springer, Berlin), p.251Google Scholar
  9. [7.B]
    Okano, K., 1984, Memoirs of the School of Sci. and Eng 48, 23;MathSciNetGoogle Scholar
  10. [7.C]
    Sakita, B., 1985,, Quantum Theory of Many Variable Systemsand Fields(World Scietific, Singapore);Google Scholar
  11. [7.d]
    Damgaard, P. H., and Huffel, H., 1987, Phys. Reports, 152, 277.CrossRefMathSciNetGoogle Scholar
  12. [8]
    Suzuki, M. 1976, Prog. Theor. Phys.56, 1454;CrossRefzbMATHADSGoogle Scholar
  13. [8.A]
    Suzuki, M., 1976, Commun. Math. Phys. 51, 183.CrossRefzbMATHADSGoogle Scholar
  14. [9]
    Huffel, H. and Rumpf, H., 1984 Phys. Letters 148B, 104;ADSMathSciNetGoogle Scholar
  15. [9.A]
    Gozzi, E., 1985, Phys. Letters, 150B, 119;ADSMathSciNetGoogle Scholar
  16. [9.B]
    Nakazato, H., and Yamanaka Y., 1986, Phys. Rev., D34, 492;ADSMathSciNetGoogle Scholar
  17. [9.C]
    Nakazato, H., 1987, Prog. Theor. Phys., 77, 20L 802L Google Scholar
  18. [10]
    Callaway, D. J. E. and Rahman, A. 1982, Phys. Rev. Letters 49, 613.CrossRefGoogle Scholar
  19. [11]
    Wigner, E. P., 1932, Phys. Rev., 40, 749.CrossRefzbMATHADSGoogle Scholar
  20. [12]
    Husimi, K. 1940 Proc. Phys. Math. Soc. Japan 22 264zbMATHGoogle Scholar
  21. [13]
    Chaturvedi S., Kapoor A. K. and Srinivasan, V., 1985, Phys. Letters, B157, 400;ADSMathSciNetGoogle Scholar
  22. [13.A]
    Ohba, I., 1986, Prog. Theor. Phys., 77, 1267.CrossRefADSGoogle Scholar
  23. [14]
    Namiki, M. and Yamanaka, Y. 1986, Prog. Theor. Phys. 75, 1447.CrossRefADSGoogle Scholar
  24. [15]
    Nakazato, N. Namiki, M., and Shibata, H. 1986 Prog. Theor. Phys. 76, 708.CrossRefADSGoogle Scholar
  25. [16]
    Grimus, W., and Huffel, H., 1983, Zeits. f. Phys., C18 129;ADSMathSciNetGoogle Scholar
  26. [16.A]
    Nakazato, H., Namiki, M., Ohba, I., and Okano, K., 1983, Prog. Theor. Phys., 70, 298.CrossRefzbMATHADSMathSciNetGoogle Scholar
  27. [17]
    Fukai, T., Hakazato, H., Ohba, I., Okano, K. and Yanamaka, Y., 1983 Prog. Theor. Phys., 69, 361;CrossRefGoogle Scholar
  28. [17.A]
    Breit, J. D., Gupta, S. and Zaks, A., 1984 Nucl. Phys., B233, 61;CrossRefADSGoogle Scholar
  29. [17.B]
    Damgaard, P. H., and Tsokos, K. 1984, Nucl. Phys., B235, 75.CrossRefADSMathSciNetGoogle Scholar
  30. [18]
    Namiki M., Ohba I., and Okano K. 1984 Prog. Theor. Phys. 72, 350.CrossRefzbMATHADSMathSciNetGoogle Scholar
  31. [19]
    Nakagoshi N., Namiki, M., Ohba, I., and Okano K. 1983 Prog. Theor. Phys., 70 326CrossRefADSGoogle Scholar
  32. [19.A]
    Zwanziger D., 1981, Nucl. Phys., B192, 259;CrossRefADSMathSciNetGoogle Scholar
  33. [19.B]
    Baulieu, L., and Zwanziger, D., 1981, Nucl. Phys., B193, 163;CrossRefADSMathSciNetGoogle Scholar
  34. [19.C]
    Seiler, E., Stematescu, I. O., and Zwanziger, D., Nucl. Phys., B239, 177Google Scholar
  35. [20]
    Fukai T., and Okano, K., 1985, Prog. Theor. Phys., 73, 790.CrossRefADSGoogle Scholar
  36. [21]
    Namiki M., Ohba, I., Okano, K., and Yanamaka, Y., 1983, Prog. Theor. Phys., 69, 1580.CrossRefzbMATHADSGoogle Scholar
  37. [22]
    Namiki, M., Ohba, I., and Tanaka, S., Yanga D. 1987, Phys. Letters, B194, 530ADSMathSciNetGoogle Scholar
  38. [23]
    Namiki, M., Ohba, I., and Tanaka, S. 1986 Phys. LettersB182, 66.ADSGoogle Scholar
  39. [24]
    For example, see: Proc. International Symp. on the Lattice Gauge Theory, held in Paris in 1987, to be published.Google Scholar
  40. [25]
    Tanaka, S., in preparation for publication.Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Mikio Namiki
    • 1
  1. 1.Department of PhysicsWaseda UniversityTokyoJapan

Personalised recommendations