Abstract
It is shown that, to a certain extent, the statistical framework of Hilbert-space quantum mechanics can be reformulated in classical terms.
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References
R. F. O'Connell, “The Wigner distribution function—50th birthday,”Found. Phys. 13, 83–92 (1983); M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, “Distribution functions in physics: Fundamentals,”Phys. Rep. 106, 121–167 (1984); E. C. G. Sudarshan, “Perception of quantum systems,” inOld and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology, A. van der Merwe, ed. (Plenum, New York, 1983), pp. 457–467.
S. T. Ali and E. Prugovečki, “Systems of imprimitivity and representations of quantum mechanics on fuzzy phase spaces,”J. Math. Phys. 18, 219–228 (1977).
S. T. Ali and E. Prugovečki, “Classical and quantum statistical mechanics in a common Liouville space,”Physica A 89, 501–521 (1977).
W. Guz, “Foundations of phase-space quantum mechanics,”Int. J. Theor. Phys. 23, 157–184 (1984); “Stochastic phase spaces, fuzzy sets, and statistical metric spaces,”Found. Phys. 14, 821–848 (1984).
F. E. Schroeck, Jr., “The transitions among classical mechanics, quantum mechanics, and stochastic quantum mechanics,”Found. Phys. 12, 825–841 (1982).
S. Gudder, “Probability manifolds,”J. Math. Phys. 25, 2397–2401 (1984); “Amplitude phase-space model for quantum mechanics,”Int. J. Theor. Phys. 24, 343–353 (1985).
I. Pitowsky, “Deterministic model of spin and statistics,”Phys. Rev. D 27, 2316–2335 (1983);Quantum Probability—Quantum Logic (Lecture Notes in Physics, Vol. 321) (Springer, Berlin, 1989).
W. Stulpe, “On the representation of quantum mechanics on phase space,”Int. J. Theor. Phys. 31, 1785–1795 (1992).
M. Singer and W. Stulpe, “Phase-space representations of general statistical physical theories,”J. Math. Phys. 33, 131–142 (1992).
P. Busch and P. J. Lahti, “The determination of the past and the future of a physical system in quantum mechanics,”Found. Phys. 19, 633–678 (1989).
P. Busch, K.-E. Hellwig, and W. Stulpe, “On classical representations of finite-dimensional quantum mechanics,”Int. J. Theor. Phys. 32, 399–405 (1993).
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Stulpe, W. Some remarks on classical representations of quantum mechanics. Found Phys 24, 1089–1094 (1994). https://doi.org/10.1007/BF02054650
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DOI: https://doi.org/10.1007/BF02054650