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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2005, Volume 250, Pages 226–261 (Mi tm40)  
This article is cited in 6 scientific papers (total in 6 papers)

Quantum Observables: An Algebraic Aspect

D. V. Treschev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (371 kB) Citations (6)
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Abstract: Quantum observables are represented as series in noncommuting generators $\hat x$ and $\hat p$. The space of such series turns out to be an infinite-dimensional associative algebra and a Lie algebra. The concept of convergence is presented for such series. In this language, quantum objects turn out to be noncommutative analogues of classical objects. Quantum analogues are proved for several basic theorems of classical mechanics.
Received in January 2005
Bibliographic databases:
Document Type: Article
UDC: 530.145
Language: Russian
Citation: D. V. Treschev, “Quantum Observables: An Algebraic Aspect”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 250, Nauka, MAIK «Nauka/Inteperiodika», M., 2005, 226–261; Proc. Steklov Inst. Math., 250 (2005), 211–244
Citation in format AMSBIB
\Bibitem{Tre05}
\by D.~V.~Treschev
\paper Quantum Observables: An Algebraic Aspect
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2005
\vol 250
\pages 226--261
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm40}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2200917}
\zmath{https://zbmath.org/?q=an:1138.81458}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 250
\pages 211--244
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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