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Finite quantum models: constructive approach to description of quantum behavior
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XIX, Tome 387 (2011), pp. 122-144 Cet article a éte moissonné depuis la source Math-Net.Ru

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Universality of quantum mechanics – its applicability to physical systems of quite different nature and scales – indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing indistinguishable, i.e. lying on the same orbit of some symmetry group, elements. In this paper we demonstrate, that quantum behavior arises naturally in systems with finite number of elements connected by nontrivial symmetry groups. The “finite” approach allows to see the peculiarities of quantum description more distinctly without need for concepts like “wave function collapse”, “Everett's multiverses” etc. In particular, under the finiteness assumption any quantum dynamics is reduced to the simple permutation dynamics. The advantage of the finite quantum models is that they can be studied constructively by means of computer algebra and computational group theory methods. 
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V. V. Kornyak. Finite quantum models: constructive approach to description of quantum behavior. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XIX, Tome 387 (2011), pp. 122-144. http://geodesic.mathdoc.fr/item/ZNSL_2011_387_a4/

[1] H. Poincaré, La valeur de la Science, Flammarion, Paris, 1904; Puankare A., O nauke, per. s fr., ed. L. S. Pontryagin, Nauka, M., 1990, 736 pp. | MR | Zbl

[2] H. Poincaré, “Les conceptions nouvelles de la matière”, Foi at vie, 15 (1912), 185–191; Puankare A., O nauke, Nauka, M., 1990 | MR | Zbl

[3] O. Nairz, M. Arndt, A. Zeilinger, “Quantum Interference Experiments with Large Molecules”, Am. J. Phys., 71:4 (2003), 319–325 | DOI

[4] V. V. Kornyak, “Quantization in Discrete Dynamical Systems”, J. Math. Sci., 168:3 (2010), 390–397 | DOI | MR | Zbl

[5] V. V. Kornyak, Structural and Symmetry Analysis of Discrete Dynamical Systems, 2010, arXiv: 1006.1754

[6] R. Feinman, A. Khibs, Kvantovaya mekhanika i integraly po traektoriyam, Mir, M., 1968

[7] M. Kholl, Teoriya grupp, IL, M., 1962

[8] http://www.gap-system.org

[9] V. Magnus, A. Karras, D. Soliter, Kombinatornaya teoriya grupp, Nauka, M., 1974 | MR | Zbl

[10] H. Weyl, “Ars Combinatoria. Appendix B”, Philosophy of Mathematics and Natural Science, Princeton University Press, 1949 ; Prikladnaya kombinatornaya matematika, Mir, M., 1968 | MR | Zbl

[11] I. R. Shafarevich, Osnovnye ponyatiya algebry, RKhD, Izhevsk, 2001

[12] N. P. Landsman, “Born Rule and its Interpretation”, Compendium of Quantum Physics, eds. Greenberger D., Hentschel K., Weinert F., Springer, 2009, 64–70 | DOI