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.
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References
Alfsen, E. M. (1971).Compact Convex Sets and Boundary Integrals, Springer-Verlag, Berlin.
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.
Ali, S. T., and Prugovečki, E. (1977).Journal of Mathematical Physics,18, 219–228.
Asimov, L., and Ellis, A. J. (1980),Convexity Theory and Its Applications in Functional Analysis, Academic Press, London.
Bugajski, S. (1991).International Journal of Theoretical Physics,30, 961–971.
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.
Busch, P. (1986).Physical Review D,33, 2253–2261.
Busch, P. J., and Lahti, P. J. (1989).Foundations of Physics,19, 633–678.
Busch, P., and Schroeck, Jr., F. E. (1989).Foundations of Physics,19, 807–872.
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.
Davies, E. B. (1976).Quantum Theory of Open Systems, Academic Press, London.
Davies, E. B., and Lewis, J. T. (1970).Communications in Mathematical Physics,17, 239–260.
Ghirardi, G. C., Rimini, A., and Weber, T. (1976).Nuovo Cimento,36B, 97–118.
Hermann, R. (1965).Journal of Mathematical Physics,6, 1768–1771.
Hermann, R. (1982).International Journal of Theoretical Physics,21, 803–828.
Hillery, M., O'Connell, R. F., Scully, M. O., and Wigner, E. P. (1984).Physics Reports,106, 121–167.
Holevo, A. S. (1982).Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam, Chapter I, §5.
Kibble, T. W. B. (1979).Communications in Mathematical Physics,65, 189–201.
Ludwig, G. (1983).Foundations of Quantum Mechanics I, Springer-Verlag, New York.
Ludwig, G. (1990).Foundations of Physics,20, 621–633.
Misra, B. (1974). InPhysical Reality and Mathematical Description, C. P. Enz and J. Mehra, eds., Reidel, Dordrecht, pp. 455–476.
Neumann, H. (1971).Communications in Mathematical Physics,23, 100–116.
Neumann, H. (1985). InRecent Development in Quantum Logic, P. Mittelstaedt and E.-W. Stachow, eds., Bibliographisches Institut, Mannheim, pp. 337–348.
O'Connell, R. F. (1988).Foundations of Physics,13, 83–92.
Prugovečki, E. (1977).International Journal of Theoretical Physics,16, 321–331.
Schaefer, H. H. (1986).Topological Vector Spaces, Springer-Verlag, New York.
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.
Stulpe, W. (1988).International Journal of Theoretical Physics,27, 587–611.
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.
Werner, R. (1983).Foundations of Physics,13, 859–881.
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On leave from the Institute of Physics, Silesian University, Katowice, Poland.
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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
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DOI: https://doi.org/10.1007/BF01215303