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Necessary and sufficient postulates of quantum mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 3, pp. 510-529 Cet article a éte moissonné depuis la source Math-Net.Ru

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We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the Hilbert space and linear operators are only secondary structures of the theory, while the primary structures are the elements of a noncommutative algebra (observables) and the functionals on this algebra, associated with the results of a single observation.
Keywords: quantum postulates, quantum measurement, physical reality.
Mots-clés : algebra of observables 
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D. A. Slavnov. Necessary and sufficient postulates of quantum mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 3, pp. 510-529. http://geodesic.mathdoc.fr/item/TMF_2005_142_3_a3/

[1] I. fon Neiman, Matematicheskie osnovy kvantovoi mekhaniki, Nauka, M., 1964 | MR

[2] I. Sigal, Matematicheskie problemy relyativistskoi fiziki, Mir, M., 1968 | MR

[3] A. Einshtein, B. Podolskii, N. Rozen, UFN, 16 (1936), 440

[4] E. Schrödinger, Naturwissenschaften, 23 (1935), 807 | DOI | Zbl

[5] D. Home, M. A. B. Whitaker, Phys. Rep., 210 (1992), 223 | DOI | MR

[6] D. A. Slavnov, TMF, 132 (2002), 434 | DOI | MR | Zbl

[7] D. A. Slavnov, TMF, 136 (2003), 437 | DOI | MR

[8] U. Rudin, Funktsionalnyi analiz, Mir, M., 1975 | MR

[9] S. Kochen, E. P. Specker, J. Math. Mech., 17 (1967), 59 | MR | Zbl

[10] A. N. Kolmogorov, Osnovnye ponyatiya teorii veroyatnostei, 2-e izd., Nauka, M., 1974 | MR

[11] Zh. Neve, Matematicheskie osnovy teorii veroyatnostei, Mir, M., 1969 | MR | Zbl

[12] Yu. V. Prokhorov, Yu. A. Rozanov, Teoriya veroyatnostei. Osnovnye ponyatiya. Predelnye teoremy. Sluchainye protsessy, Spravochnik, Nauka, M., 1967 | MR | Zbl

[13] Zh. Emkh, Algebraicheskii podkhod v statisticheskoi mekhanike i kvantovoi teorii polya, Mir, M., 1976

[14] Zh. Diksme, $C^*$-algebry i ikh predstavleniya, Nauka, M., 1974 | MR

[15] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1984 | MR

[16] H. Everett, Rev. Mod. Phys., 29 (1957), 454 | DOI | MR