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The A. D. Alexandrov's Axiomatizations of Quantum Mechanics and Relativity Theory
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 3, pp. 61-72 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the article the A.D. Alexandrov's results on quantum mechanics and special theory of relativity are presented in axiomatic form.
Keywords: axiomatics, A. D. Alexandrov, quantum mechanics, relativity theory. 
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A. K. Guts. The A. D. Alexandrov's Axiomatizations of Quantum Mechanics and Relativity Theory. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 3, pp. 61-72. http://geodesic.mathdoc.fr/item/VNGU_2012_12_3_a5/

[1] Aleksandrov A. D., “O vychislenii energii dvukhvalentnogo atoma po metodu Foka”, Zhurn. eksperim. i teoret. fiziki, 4:4 (1936), 326–341

[2] Aleksandrov A. D., “Zamechanie o pravilakh kommutatsii i uravnenii Shredingera”, Dokl. AN SSSR, 4:4 (1934), 198–202 | Zbl

[3] Gilbert D., Bernais P., Osnovaniya matematiki. Logicheskie ischisleniya i formalizatsiya arifmetiki, Nauka, M., 1975 | MR

[4] Aleksandrov A. D., “O smysle volnovoi funktsii”, Dokl. AN SSSR, 85:2 (1952), 291–294 | Zbl

[5] Aleksandrov A. D., “O paradokse Einshteina v kvantovoi mekhanike”, Dokl. AN SSSR, 84:2 (1952), 253–256 | Zbl

[6] Einstein A., “Zur Elektrodynamik der Bewegter Körper”, Ann. Phys., 17 (1905), 891–921 | DOI | Zbl

[7] Ignatowsky W., “Der Starre Körper und das Relativitätsprinzip”, Annalen der Physik, 338:13 (1910), 607–630 | DOI

[8] Umov N. A., “Edinoobraznyi vyvod preobrazovanii, sovmestnykh s printsipom otnositelnosti”: Umov N. A., Izbr. soch., Gostekhizdat, M., 1950

[9] Robb A. A., A Theory of Time and Space, Heffer, Cambridge, 1912

[10] Weyl H., Raum, Zeit, Materie, Berlin, 1923

[11] Weyl H., Axiomatik, Rukopis lektsii po aksiomatike STO 1930–31 gg., khranyaschayasya v Institute for Advanced Study at Princeton

[12] Carathéodory C., “Zur Axiomatik der Speziellen Relativitatstheorie”, Sitzb. Preuss. Acad. Wiss., 1923, 12–27

[13] Reichenbach H., Axiomatization of the Theory of Relativity, Univ. Calif. Press, Berkely and Los Angeles, 1969; 1-е издание, 1924

[14] Fok V. A., Teoriya prostranstva, vremeni i tyagoteniya, M., 1955, 475–482

[15] Landau L. D., Lifshits E. M., Teoriya polya, Nauka, M., 1973

[16] Zeeman E. C., “Causality Implies the Lorentz Group”, J. Math. Phys., 5:4 (1964), 490–493 | DOI | MR | Zbl

[17] Aleksandrov A. D., “Prostranstvo i vremya v sovremennoi fizike v svete filosofskikh idei Lenina”, Lenin i sovremennoe estestvoznanie, Mysl, M., 1969, 202–229

[18] Aleksandrov A. D., “K osnovaniyam geometrii prostranstva-vremeni”, Dokl. AN SSSR, 219:1 (1974), 11–14 | Zbl

[19] Aleksandrov A. D., “K osnovaniyam geometrii prostranstva-vremeni”, Dokl. AN SSSR, 219:2 (1974), 265–267 | Zbl

[20] Guts A. K., Khronogeometriya, OOO «UniPak», Omsk, 2008 | MR

[21] Aleksandrov A. D., “Ob osnovakh teorii otnositelnosti”, Vestn. LGU. Ser. mat., 1976, no. 19, 5–28 | Zbl

[22] Morris M. S., Thorne K. S., “Wormholes in Spacetime and Their Use for Interstellar Travel: A Tool Teaching General Relativity”, Am. J. Phys., 56:5 (1988), 395–412 | DOI | MR | Zbl

[23] Morris M. S., Thorne K. S., Yurtsever U., “Wormholes, Time Machines, and the Weak Energy Condition”, Phys. Rev. Lett., 61:13 (1988), 1446–1449 | DOI

[24] Pimenov R. I., “Prostranstva kinematicheskogo tipa”, Zap. nauch. seminara LOMI, 6, 1968, 3–496

[25] Busemann H., “Time-Like Spaces”, Dissertationes mathematicae, 1967, no. 53, 5–50 | MR

[26] Kronheimer T.Ḣ., Penrose R., “On the Structure of Causal Spaces”, Proc. Cambr. Phil. Soc., 63 (1967), 481–501 | DOI | MR | Zbl

[27] Quinn F., “Ends of Maps”, J. Diff. Geom., 17:3 (1982), 503–521 | MR | Zbl

[28] Freedman M., “Topology of 4-Dimensional Manifolds”, J. Diff. Geom., 17:3 (1982), 357–453 | MR | Zbl

[29] Guts A. K., “Khronogeometriya i ekzoticheskie $\mathbb{R}^4$”, Vsesoyuznaya konferentsiya po geometrii «v tselom», Tezisy dokladov, IM SO AN SSSR, Novosibirsk, 1987, 36

[30] Guts A. K., “O vremenipodobnykh zamknutykh gladkikh krivykh v obschei teorii otnositelnosti”, Izv. vuzov. Fizika, 1973, no. 9, 33–36

[31] Goldblatt R., Orthogonality and Spacetime Geometry, Springer, N. Y., 1987 | MR | Zbl

[32] Székely G., The Existence of Superluminal Paricles is Consistent with the Kinematics of Einstein's Special Theoty of Relativity, arXiv: 1202.5790v1

[33] Guts A. K., “Teoretiko-toposnyi podkhod k osnovaniyam teorii otnositelnosti”, Dokl. AN SSSR, 318:6 (1991), 1294–1297 | MR | Zbl

[34] P. S. Aleksandrov (red.), Problemy Gilberta, Sb. nauch. tr., Nauka, M., 1969 | MR

[35] Einshtein A., “Geometriya i opyt”: Einshtein A., Sobr. nauch. tr., v. 4, Nauka, M., 1966