Stochastic Processes - Quantum Physics

  • L. Streit
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 26/1984)


It is now about 20 years ago that I first spoke about Wiener Integrals at one of the earliest Schladming Winter Schools. As I was assembling my notes for those lectures one of my senior colleagues remarked that Functional Integrals provided a nice reformulation of Quantum Theory, but really there was hardly anything you could do with them that one had not already done otherwise.


Brownian Motion Random Walk White Noise Characteristic Function Stochastic Differential Equation 


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  1. 1.
    B. Mandelbrot, “Fractals. Form, Chance and Dimension” (Freeman, San Francisco, 1978).Google Scholar
  2. 2.
    T. Hida, “Brownian Motion”, Applications of Mathematics, Vol.11 (Springer, Berlin, 1980).Google Scholar
  3. 3.
    S. Albeverio, R. Høegh-Krohn, L. Streit, “Energy Forms, Hamiltonians, and Distorted Brownian Paths”, J. Math. Phys. 18 (1977) 907.CrossRefMATHADSGoogle Scholar
  4. 4.
    S. Albeverio, R. Høegh-Krohn, L. Streit, “Regularization of Hamiltonians and Processes”, J. Math. Phys. 21 (1980) 1636.CrossRefMATHADSMathSciNetGoogle Scholar
  5. 5.
    J.M. Gelfand, N.Ya. Vilenkin, “Generalized Functions”, Vol.4 (Academic Press, New York, 1964).Google Scholar
  6. 6.
    J. Holtsmark, “Über die Verbreitung von Spektrallinien”, Ann. d. Physik 58 (1919) 577.CrossRefADSGoogle Scholar
  7. 7.
    W. Feller, “An Introduction to Probability Theory and its Applications”, 2nd ed. (Wiley, New York, 1971).MATHGoogle Scholar
  8. 8.
    S. Chandrasekhar, “Stochastic Problems in Physics and Astronomy”, Rev. Mod. Phys. 15 (1943) 1.CrossRefMATHADSMathSciNetGoogle Scholar
  9. 9.
    A. Khinchin, “Mathematical Foundations of Statistical Mechanics” (1949).MATHGoogle Scholar
  10. 10.
    J. Cassandro, G. Jona-Lasinio, “Many Degrees of Freedom-Field Theory” (Plenum, 1978), p.54 ff.Google Scholar
  11. 11.
    T. Hida, “Stationary Stochastic Processes” (Princeton University Press, Princeton, 1970).MATHGoogle Scholar
  12. 12.
    E. Nelson, “Dynamical Theories of Brownian Motion” (Princeton University Press, Princeton, 1967).MATHGoogle Scholar
  13. 13.
    C. DeWitt-Morette, K.D. Elworthy, “New Stochastic Methods in Physics”, Physics Reports 77 (1981) 121–382.CrossRefADSGoogle Scholar
  14. H. Ezawa, J.R. Klauder, L.A. Shepp, “A Path Space Picture for Feynman-Kac Averages, Ann. Phys. 88 (1974) 588.CrossRefMATHADSMathSciNetGoogle Scholar
  15. 14.
    Y. Higuchi, in “Field Theory — Algebras, Processes” (Springer, Vienna, 1980).Google Scholar
  16. 15.
    S. Albeverio, M. Fukushima, W. Karwowski, L. Streit, “Capacity and Quantum-Mechanical Tunneling”, Comm. Math. Phys. 81 (1981) 501.CrossRefMATHADSMathSciNetGoogle Scholar
  17. 16.
    M. Fukushima, “Dirichlet Forms and Markov Processes” (North-Holland/Kodansha, Amsterdam/Tokyo, 1980).MATHGoogle Scholar
  18. 17.
    S. Albeverio, R. Høegh-Krohn, “Topics in Infinite- Dimensional Analysis”, in “Lectures Notes in Physics”, Vol. 80 (Springer, Berlin, 1978).Google Scholar

Further References in this Field are

  1. L. Breiman, “Probability” (Addison-Wesley, Reading 1968).MATHGoogle Scholar
  2. C. Carvalho, E. Ribeiro, L. Streit, “Stochastic Processes – Mathematics and Physics. An Introduction”(CFMC, Lissabon, 1984).Google Scholar
  3. J.L. Doob, “Stochastic Processes” (Wiley, New York, 1953).MATHGoogle Scholar
  4. E.B. Dynkin, “Markov processes” (Springer, 1965).MATHGoogle Scholar
  5. M.I. Freidlin, “Markov processes and differential equations”. Progress in Math. III (Plenum Press, N.Y., 1969).Google Scholar
  6. A. Friedman, “Stochastic differential equations and its applications”, Vol.1 and II (N.Y., Academic Press, 1975).Google Scholar
  7. N.G. van Kampen, “Stochastic Processes in Physics and Chemistry” (North Holland, Amsterdam, 1983).Google Scholar
  8. P. Levy, “Processus Stochastiques et mouvement brownien”, 2eme ed. (Gauthier-Villars, Paris, 1956).Google Scholar
  9. E. Lukacs, “Characteristic functions”, 2nd. ed. (Griffin, London, 1970).MATHGoogle Scholar
  10. M. Rosenblatt, “Random Processes” (Springer, Berlin, 1974).CrossRefMATHGoogle Scholar
  11. B. Simon, “Functional Integration and Quantum Physics”(Academic Press, 1979).MATHGoogle Scholar
  12. J. Glimm, A. Jaffe, “Quantum Physics” (Springer,1981).MATHGoogle Scholar
  13. G. Jona-Lasinio, “The Renormalization Group — A probabilistic view”, Nuovo Cim. 26B (1975) 99.CrossRefADSMathSciNetGoogle Scholar
  14. G. Jona-Lasinio, “Stochastic Dynamics and the Semi-Classical Limit of Quantum Mechanics”, in “Quantum Fields — Algebras, Processes” (L. Streit, ed.)(Springer, Vienna, 1980).Google Scholar
  15. E. Lieb, “Monotonicity of the molecular electronic energy in the nuclear coordinates”, J. Phys. B15 (1982) L63.ADSGoogle Scholar
  16. M. Reed, “Functional Analysis and Probability Theory”, in “Constructive Quantum Field Theory”, G. Velo, A. Nightman, ed., Lectures Notes in Physics, Vol. 25 (Springer, Berlin, 1973).CrossRefGoogle Scholar
  17. L. Streit, “Energy Forms: Schrödinger Theory Processes”, Physics Reports. 11 (1980).Google Scholar
  18. K. Symanzik, “Euclidean Quantum Field Theory”, in “Local Quantum Field Theory”, R. Jost, ed., Academic Press, 1969).Google Scholar
  19. R.L. Dobrushin, “Automodel generalized Random Fields and their Renormalization Group”, Ann. Prob. (1979) 1.Google Scholar
  20. D. Dürr, S. Goldstein, J.L. Lebowitz, “Stochastic Processes Orginating in Deterministic Microscopic Dynamics”, Journ. Statist, Phys. 30 (1983) 519.CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • L. Streit
    • 1
  1. 1.BiBoSUniversität BielefeldBielefeldFR Germany

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