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Teoreticheskaya i Matematicheskaya Fizika, 1977, Volume 30, Number 1, Pages 6–11 (Mi tmf2687)  
This article is cited in 6 scientific papers (total in 6 papers)

On admissible forms of canonical mechanics

Yu. M. Shirokov
Full-text PDF (703 kB) Citations (6)
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Abstract: General solution has been derived for the functional $c$-number equation which determines all admissible realisations of yarious mechanics with associative (but not necessary realisable by operators) law of multiplication of the observables. The general solution includes the algebras of observables for the classical and for the quantum mechanics. In addition, the solution includes one new algebra which corresponds formally to purely imaginary value fo the Planck constant. The mathematical difficulties of treating the new algebra are discussed.
Received: 28.05.1976
English version:
Theoretical and Mathematical Physics, 1977, Volume 30, Issue 1, Pages 3–6
DOI: https://doi.org/10.1007/BF01029352
Bibliographic databases:
Language: Russian
Citation: Yu. M. Shirokov, “On admissible forms of canonical mechanics”, TMF, 30:1 (1977), 6–11; Theoret. and Math. Phys., 30:1 (1977), 3–6
Citation in format AMSBIB
\Bibitem{Shi77}
\by Yu.~M.~Shirokov
\paper On admissible forms of canonical mechanics
\jour TMF
\yr 1977
\vol 30
\issue 1
\pages 6--11
\mathnet{http://mi.mathnet.ru/tmf2687}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=441107}
\zmath{https://zbmath.org/?q=an:0399.70004|0436.70002}
\transl
\jour Theoret. and Math. Phys.
\yr 1977
\vol 30
\issue 1
\pages 3--6
\crossref{https://doi.org/10.1007/BF01029352}
Linking options:
  • https://www.mathnet.ru/eng/tmf2687
  • https://www.mathnet.ru/eng/tmf/v30/i1/p6
    • This publication is cited in the following 6 articles:
    1. A. A. Magazev, A. S. Popov, I. V. Shirokov, “Constructing Invariant Differential Operators on Homogeneous Spaces Using the Star Product”, Russ Phys J, 64:10 (2022), 1783  crossref
    2. G. K. Tolokonnikov, “On observable algebras of a class of associative mechanical systems”, Theoret. and Math. Phys., 63:2 (1985), 433–439  mathnet  crossref  mathscinet  zmath  isi
    3. G. K. Tolokonnikov, “Algebras of observables of nearly canonical physical theories. I”, Theoret. and Math. Phys., 60:1 (1984), 690–693  mathnet  crossref  mathscinet  zmath  isi
    4. G. K. Tolokonnikov, “Algebras of observables of nearly canonical physical theories. II”, Theoret. and Math. Phys., 61:2 (1984), 1072–1077  mathnet  crossref  mathscinet  isi
    5. G. K. Tolokonnikov, “Hamiltonian algebras”, Theoret. and Math. Phys., 37:3 (1978), 1057–1065  mathnet  crossref  mathscinet  zmath
    6. G. K. Tolokonnikov, “Associative Hamiltonian algebras”, Theoret. and Math. Phys., 31:2 (1977), 441–445  mathnet  crossref  mathscinet  zmath
    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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    Abstract page:309
    Full-text PDF :119
    References:52
    First page:1
     
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