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Tensor product of generalized sample spaces

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Abstract

The tensor product of generalized samples spacer or manuals is defined within the framework of empirical logic The requirement to accurately reflect the interaction of experimental procedures for coupled systems leads to three levels of product: the cross-product, operational product, and tensor product. The structure of the weights of these products is examined and is used to give a condition for the existence of the tensor product Categorical properties of the tensor product, including a universal mapping theorem, are given.

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References

  1. Dirac, P. A. M. (1958).The Principles of Quantum Mechanics, 4th ed., International Series of Monographs on Physics. Oxford University Press, Oxford.

  2. Foulis, D. J, and Randall, C. H. (1979). Empirical Logic and tensor products. Proceedings of the Colloquium on the Interpretations and Foundations of Quantum Theories, Fachbereich Physik der Philipps Universität, Marburg, West Germany, May 1979, H. Neumann, ed. to appear.

  3. Kolmogorov, A. N. (1956).Foundations of the Theory of Probability, 2nd ed., Chelsea Publishing Co., New York.

  4. Lock, P. F. (1981). Categories of manuals, Ph.D. dissertation, University of Massachusetts.

  5. Lock, R. H. (1981). Constructing the Tensor Product of Generalized Sample Spaces, Ph.D. dissertation, University of Massachusetts.

  6. Randall, C. H., and Foulis, D. J. (1979). Operational statistics and tensor products, Proceedings of the Colloquium on the Interpretations and Foundations of Quantum Theories, Fachbereich Physik der Philipps Universität, Marburg, West Germany, May 1979.

  7. Randall, C. H., and Foulis, D. J. (1978). The operatonal approach to quantum mechanics, inThe Logico-Algebraic Approach to Quantum Mechanics III, C. A. Hooker, ed. Reidel Publishing Co., Dordrecht, Holland.

  8. von Neumann, J. (1955).The Mathematical Foundations of Quantum Mechanics (Springer, Berlin, 1932), translated by R. T. Beyer. Princeton University Press Princeton, New Jersey.

  9. Zecca, A. (1978). On the coupling of logics,Journal of Mathematical Physics,19, 6.

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Lock, P.F., Lock, R.H. Tensor product of generalized sample spaces. Int J Theor Phys 23, 629–641 (1984). https://doi.org/10.1007/BF02214134

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Keywords

  • Weight Function
  • Tensor Product
  • Operational Product
  • Categorical Property
  • Product Weight