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Quantum Mechanics of Systems with a Nonenumerable Number of Degrees of Freedom

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Abstract

Is has been shown that the quantum theory of systems with an infinite nonenumerable number of degrees of freedom is incompatible with the assumption about the continuity of the space of indices of degrees of freedom: in this case, a discrete topology on the space of indices is required. This is illustrated by the example of field systems.

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REFERENCES

  1. G. Goldstein, Classical Mechanics [in Russian]. Moscow, Gostekhizdat (1957).

    Google Scholar 

  2. S. S. Sannikov-Proskuryakov, Izv. Vyssh. Ucheb. Zaved., 11, 52-61 (1999); Ukr. Fiz. Zh., 45, 639–642; 778–780 (2000); 46, 5–13; 138–147 (2001).

    Google Scholar 

  3. J. von Neumann, Proc. Nat. Acad. Sci. US., 22, 92-100. (1936).

    Google Scholar 

  4. N. N. Bogolyubov, A. A. Logunov, and I. T. Todorov, Foundations of the Axiomatic Approach in Quantum Field Theory [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  5. J. von Neumann, Mathematical Foundations of Quantum Mechanics [Russian translation], Nauka, Moscow (1964).

    Google Scholar 

  6. P. A. M. Dirac, Principles of Quantum Mechanics [Russian translation], Nauka, Moscow (1969).

    Google Scholar 

  7. J. von Neumann, Math Ann., 104, 570-578 (1931)

    Google Scholar 

  8. H. Bohr, Almost Periodic Functions [Russian translation], Gostekhizdat, Moscow (1934).

    Google Scholar 

  9. L. S. Pontrjagin, Continuous Groups [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  10. J. von Neumann, Trans. Amer. Math. Soc., 36, 445-492 (1934).

    Google Scholar 

  11. L. Gording and A. S. Wightman, Proc. Nat. Acad. Sci. (USA), 40, 617 (1954).

    Google Scholar 

  12. S. S. Sannikov-Proskuryakov, Ukr. Fiz. Zh., 7, 805-808 (1999); 6, 638–641; 7, 778–780 (2000); 2, 138–147; 3, 263–271 (2000).

    Google Scholar 

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  1. National Scientific Center Kharkov Physicotechnical Institute, Russia

    S. S. Sannikov-Proskuryakov

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  1. S. S. Sannikov-Proskuryakov
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Sannikov-Proskuryakov, S.S. Quantum Mechanics of Systems with a Nonenumerable Number of Degrees of Freedom. Russian Physics Journal 44, 863–868 (2001). https://doi.org/10.1023/A:1013659920245

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  • DOI: https://doi.org/10.1023/A:1013659920245

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