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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 ˆx and ˆp. 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{http://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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  • https://www.mathnet.ru/eng/tm/v250/p226
    • This publication is cited in the following 6 articles:
    1. V. V. Kozlov, “Quadratic conservation laws for equations of mathematical physics”, Russian Math. Surveys, 75:3 (2020), 445–494  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. V. V. Kozlov, “Linear systems with quadratic integral and complete integrability of the Schrödinger equation”, Russian Math. Surveys, 74:5 (2019), 959–961  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Anikin A., “Non-commutative normal form, spectrum and inverse problem”, Asymptotic Anal., 101:4 (2017), 207–225  crossref  mathscinet  zmath  isi  scopus
    4. A. Yu. Anikin, “Quantum Birkhoff normal forms”, Theoret. and Math. Phys., 160:3 (2009), 1274–1291  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Anikin, A, “Normal Form of a Quantum Hamiltonian with One and a Half Degrees of Freedom Near a Hyperbolic Fixed Point”, Regular & Chaotic Dynamics, 13:5 (2008), 377  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. D. V. Treschev, “Noncommutative Structures”, Proc. Steklov Inst. Math., 259 (2007), 196–235  mathnet  crossref  mathscinet  zmath  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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