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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 129, Number 1, Pages 87–102
DOI: https://doi.org/10.4213/tmf521 (Mi tmf521) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Statistical Algebraic Approach to Quantum Mechanics

D. A. Slavnov

M. V. Lomonosov Moscow State University
Full-text PDF (254 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf521
Abstract: A scheme for constructing quantum mechanics not based on the Hilbert space and linear operators as primary elements of the theory is proposed. A particular variant of the algebraic approach is discussed. The elements of a noncommutative algebra (i.e., the observables) and the nonlinear functionals on this algebra (i.e., the physical states) serve as the primary components of the theory. The functionals are associated with the results of a single measurement. The ensembles of physical states are suggested for the role of quantum states in the standard quantum mechanics. It is shown that the mathematical formalism of the standard quantum mechanics can be fully recovered within this scheme.
Received: 06.02.2001
Revised: 03.04.2001
English version:
Theoretical and Mathematical Physics, 2001, Volume 129, Issue 1, Pages 1385–1397
DOI: https://doi.org/10.1023/A:1012419528129
Bibliographic databases:
Language: Russian
Citation: D. A. Slavnov, “Statistical Algebraic Approach to Quantum Mechanics”, TMF, 129:1 (2001), 87–102; Theoret. and Math. Phys., 129:1 (2001), 1385–1397
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf521
  • https://doi.org/10.4213/tmf521
  • https://www.mathnet.ru/eng/tmf/v129/i1/p87
    • This publication is cited in the following 5 articles:
    1. D. A. Slavnov, “Algebraic and Statistical Methods in Quantum and Gravitational Physics”, Phys. Part. Nuclei, 53:3 (2022), 706  crossref
    2. Zorin A.V., “Operatsionnaya model kvantovykh izmerenii kuryshkina-vudkevicha”, Vestnik Rossiiskogo universiteta druzhby narodov. Seriya: Matematika, informatika, fizika, 2012, no. 2, 43–55 The operational model of quantum measurement of kuryshkin-wodkiewicz  elib
    3. Slavnov DA, “Measurements and mathematical formalism of quantum mechanics”, Physics of Particles and Nuclei, 38:2 (2007), 147–176  crossref  adsnasa  isi  scopus  scopus
    4. Slavnov DA, “Concept of objective local reality in quantum theory”, Physics of Particles and Nuclei, 36 (2005), S24–S27, Suppl. 1  isi
    5. D. A. Slavnov, “Quantum Mechanics as a Complete Physical Theory”, Theoret. and Math. Phys., 132:3 (2002), 1264–1276  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Full-text PDF :288
    References:61
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