Hilbertian interpretations of manuals
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- by Stanley P. Gudder PDF
- Proc. Amer. Math. Soc. 85 (1982), 251-255 Request permission
Abstract:
We characterize manuals which admit an interpretation in a manual on a Hilbert space. This characterization is given in terms of a certain set of states that the manual supports.References
- D. J. Foulis and C. H. Randall, Operational statistics. I. Basic concepts, J. Mathematical Phys. 13 (1972), 1667–1675. MR 416417, DOI 10.1063/1.1665890 —, Empirical logic and quantum mechanics, Synthese 29 (1974), 81-111.
- D. J. Foulis and C. H. Randall, The empirical logic approach to the physical sciences, Foundations of quantum mechanics and ordered linear spaces (Advanced Study Inst., Marburg, 1973) Lecture Notes in Phys., Vol. 29, Springer, Berlin, 1974, pp. 230–249. MR 0479146
- D. J. Foulis and C. H. Randall, Manuals, morphisms and quantum mechanics, Mathematical foundations of quantum theory (Proc. Conf., Loyola Univ., New Orleans, La., 1977) Academic Press, New York, 1978, pp. 105–126. MR 0495822
- Stanley P. Gudder, Stochastic methods in quantum mechanics, North-Holland Series in Probability and Applied Mathematics, North-Holland, New York-Oxford, 1979. MR 543489
- Josef M. Jauch, Foundations of quantum mechanics, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1968. MR 0218062 G. Mackey, The mathematical foundations of quantum mechanics, Benjamin, New York, 1963.
- C. H. Randall and D. J. Foulis, Operational statistics. II. Manuals of operations and their logics, J. Mathematical Phys. 14 (1973), 1472–1480. MR 416418, DOI 10.1063/1.1666208 —, A mathematical setting for inductive reasoning, in Foundations of Probability Theory, Statistical Inference and Statistical Theories of Science (C. A. Hooker, Ed.), Reidel, Dordrecht, 1976. —, The operational approach to quantum mechanics, in The Logico-Algebraic Approach to Quantum Mechanics (C. A. Hooker, Ed.), Reidel, Dordrecht, 1977.
- V. S. Varadarajan, Geometry of quantum theory. Vol. I, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1968. MR 0471674
- Ron Wright, Spin manuals: empirical logic talks quantum mechanics, Mathematical foundations of quantum theory (Proc. Conf., Loyola Univ., New Orleans, La., 1977) Academic Press, New York, 1978, pp. 177–254. MR 0503049
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 251-255
- MSC: Primary 81B10; Secondary 03G12, 06C99
- DOI: https://doi.org/10.1090/S0002-9939-1982-0652452-9
- MathSciNet review: 652452