Skip to main content

On the problem of non configurational observables in stochastic mechanics

  • 502 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1055)

Keywords

  • Uncertainty Relation
  • Canonical Commutation Relation
  • Stochastic Mechanic
  • Dirac Field
  • Stochastic Acceleration

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. Nelson: "Connection between Brownian Motion and Quantum Mechanics" in "Einstein Symposium, Berlin", H. Nelkonski, A. Hermann, H. Poser eds. Springer-Verlag 1979

    Google Scholar 

  2. F. Guerra: "Structural Aspects of Stochastic Mechanics and Stochastic Field Theory" in "New Stochastic Methods in Physics", C. De witt-Morette, K.D. Elworthy eds. Phys. Reports 77 (1981)

    Google Scholar 

  3. S. Albeverio, Ph. Combe, M. Sirugue-Collin eds:"Stochastic Processes in Quantum Theory and Statistical Physics".

    Google Scholar 

  4. R.P. Feynman, M. Gell-Mann: "Theory of the Fermi Interaction" Phys. Rev. 109, 193 (1958)

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  5. E. Nelson: "The Use of the Wiener Process in Quantum Theory" in "Collected Works of Norbert Wiener" P. Masani ed. M.I.T. Press (1979)

    Google Scholar 

  6. F. Guerra, L. Morato: "Momentum-Position Complementarity in Stoch. Mech."; in Ref. 3

    Google Scholar 

  7. D. de Falco, F. Guerra: "On the Local Structure of the Euclidean Dirac Field", Journ. Math. Phys. 21 1111 (1980)

    CrossRef  ADS  MathSciNet  Google Scholar 

  8. J. Schwinger: "Euclidean Quantum Electrodynamics" Phys. Rev. 115, 721 (1959)

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  9. G.F. De Angelis, D. de Falco, F. Guerra: "Probabilistic Ideas for Fermi Fields", Phys. Rev. D 23, 1747 (1981)

    ADS  Google Scholar 

  10. G.F. De Angelis, D. de Falco, F. Guerra: "Stochastic Processes and Fermi Fields", contribution to Ref. 1.

    Google Scholar 

  11. P. Jordan, E. Wigner: "Uber das Paulische Aquivalentzverbot", Zeit. für Physik 47, 631 (1928)

    CrossRef  ADS  MATH  Google Scholar 

  12. L. de La Pena-Auerbach, M. Cetto: "Stronger Form for the Position-Momentum Uncertainty Relation" Phys. Lett. 39A, 65 (1972)

    CrossRef  ADS  MathSciNet  Google Scholar 

  13. D. de Falco, S. De Martino, S. De Siena: "Position-Momentum Uncertainty Relation in Stochastic Mechanics" Phys. Rev. Lett. 49, 181 (1982)

    CrossRef  ADS  MathSciNet  Google Scholar 

  14. R.P. Feynman, A.R. Hibbs: "Quantum Mechanics and Path Integrals". Mc Graw-Hill 1965.

    Google Scholar 

  15. D. Shucker: "Stochastic Mechanics" Princeton Thesis (1978), and Journ. Funct. Analysis 38, 146 (1980)

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. D. de Falco, S. De Martino, S. De Siena: "Momentum from Sample Paths in Stochastic Mechanics" to be published in Lettere al Nuovo Cimento

    Google Scholar 

  17. N.J. Rao, J.D. Borwankar, D. Ramkrishna: "Numerical Solution of Ito Integral Equations" SIAM Journ. Control. 12, 124 (1974)

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. L. Smolin: "On the Nature of Quantum Fluctuations and their Relation to Gravitation and the Principle of Inertia" I.A.S. Preprint, Princeton (1982)

    Google Scholar 

  19. J.B. Hartle, S.W. Hawking: "Path Integral Derivation of Black-hole Radiance" Phys. Rev. D13, 2188 (1978)

    ADS  Google Scholar 

  20. J.H. Eberly, L.P.S. Singh: "Time Operators, Partial Stationarity, and the Energy-time Uncertainty Relation". Phys. Rev. D7, 359 (1982)

    ADS  Google Scholar 

  21. C.H. Blanchard: "Density Matrix and Energy-time Uncertainty" Am. Journ. Phys. 50, 642 (1982)

    CrossRef  ADS  Google Scholar 

  22. L. Mandelstam, I. Tamm: J. Phys. (USSR) 9, 249 (1945)

    MathSciNet  Google Scholar 

  23. S. De Martino, S. De Siena: "On Uncertainty Relations in Stochastic Mechanics" Salerno, Preprint (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

de Falco, D. (1984). On the problem of non configurational observables in stochastic mechanics. In: Accardi, L., Frigerio, A., Gorini, V. (eds) Quantum Probability and Applications to the Quantum Theory of Irreversible Processes. Lecture Notes in Mathematics, vol 1055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071714

Download citation

  • DOI: https://doi.org/10.1007/BFb0071714

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12915-8

  • Online ISBN: 978-3-540-38798-5

  • eBook Packages: Springer Book Archive