Skip to main content
Log in

Classical frames for a quantum theory — A bird's-eye view

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

All proposals of phase-space models for quantum mechanics are classified into two well-defined classes and then described in terms of operational statistical theories. The extreme generality of the description, devoid of unessential details, leads to almost trivial proofs of many facts discovered elsewhere with great effort. A new proposal of quantization is briefly sketched.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Alfsen, E. M. (1971).Compact Convex Sets and Boundary Integrals, Springer-Verlag, Berlin.

    Google Scholar 

  • Ali, S. T., and Doebner, H. D. (1986). InThe Physics of Phase Space, Y. S. Kim and W. W. Zachary, eds., Springer-Verlag, Berlin, pp. 330–346.

    Google Scholar 

  • Ali, S. T., and Prugovečki, E. (1977).Journal of Mathematical Physics,18, 219–228.

    Google Scholar 

  • Asimov, L., and Ellis, A. J. (1980),Convexity Theory and Its Applications in Functional Analysis, Academic Press, London.

    Google Scholar 

  • Bugajski, S. (1991).International Journal of Theoretical Physics,30, 961–971.

    Google Scholar 

  • Bugajski, S., Busch, P., Cassinelli, G., Lahti, P. J., and Quadt, R. (1993). Probability structures for quantum state spaces,Reviews in Mathematical Physics, in press.

  • Busch, P. (1985).International Journal of Theoretical Physics,24, 63–92.

    Google Scholar 

  • Busch, P. (1986).Physical Review D,33, 2253–2261.

    Google Scholar 

  • Busch, P. J., and Lahti, P. J. (1989).Foundations of Physics,19, 633–678.

    Google Scholar 

  • Busch, P., and Schroeck, Jr., F. E. (1989).Foundations of Physics,19, 807–872.

    Google Scholar 

  • Busch, P., Hellwig, K.-E., and Stulpe, W. (1991). On classical representations of finite-dimensional quantum mechanics, preprint.

  • Cirelli, R., and Lanzavecchia, P. (1984).Nuovo Cimento,79B, 271–283.

    Google Scholar 

  • Davies, E. B. (1976).Quantum Theory of Open Systems, Academic Press, London.

    Google Scholar 

  • Davies, E. B., and Lewis, J. T. (1970).Communications in Mathematical Physics,17, 239–260.

    Google Scholar 

  • Ghirardi, G. C., Rimini, A., and Weber, T. (1976).Nuovo Cimento,36B, 97–118.

    Google Scholar 

  • Hermann, R. (1965).Journal of Mathematical Physics,6, 1768–1771.

    Google Scholar 

  • Hermann, R. (1982).International Journal of Theoretical Physics,21, 803–828.

    Google Scholar 

  • Hillery, M., O'Connell, R. F., Scully, M. O., and Wigner, E. P. (1984).Physics Reports,106, 121–167.

    Google Scholar 

  • Holevo, A. S. (1982).Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam, Chapter I, §5.

    Google Scholar 

  • Kibble, T. W. B. (1979).Communications in Mathematical Physics,65, 189–201.

    Google Scholar 

  • Ludwig, G. (1983).Foundations of Quantum Mechanics I, Springer-Verlag, New York.

    Google Scholar 

  • Ludwig, G. (1990).Foundations of Physics,20, 621–633.

    Google Scholar 

  • Misra, B. (1974). InPhysical Reality and Mathematical Description, C. P. Enz and J. Mehra, eds., Reidel, Dordrecht, pp. 455–476.

    Google Scholar 

  • Neumann, H. (1971).Communications in Mathematical Physics,23, 100–116.

    Google Scholar 

  • Neumann, H. (1985). InRecent Development in Quantum Logic, P. Mittelstaedt and E.-W. Stachow, eds., Bibliographisches Institut, Mannheim, pp. 337–348.

    Google Scholar 

  • O'Connell, R. F. (1988).Foundations of Physics,13, 83–92.

    Google Scholar 

  • Prugovečki, E. (1977).International Journal of Theoretical Physics,16, 321–331.

    Google Scholar 

  • Schaefer, H. H. (1986).Topological Vector Spaces, Springer-Verlag, New York.

    Google Scholar 

  • Singer, M., and Stulpe, W. (1991). Phase-space representations of general statistical physical theories, preprint.

  • Souriau, J.-M. (1983).Foundations of Physics,13, 133–151.

    Google Scholar 

  • Stulpe, W. (1988).International Journal of Theoretical Physics,27, 587–611.

    Google Scholar 

  • Sudarshan, E. C. G. (1983). InOld and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology, A. van der Merwe, ed., Plenum Press, New York.

    Google Scholar 

  • Werner, R. (1983).Foundations of Physics,13, 859–881.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

On leave from the Institute of Physics, Silesian University, Katowice, Poland.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bugajski, S. Classical frames for a quantum theory — A bird's-eye view. Int J Theor Phys 32, 969–977 (1993). https://doi.org/10.1007/BF01215303

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01215303

Keywords

Navigation