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TMF, 2013, Volume 174, Number 2, Pages 285–291 (Mi tmf8411)  

This article is cited in 1 scientific paper (total in 1 paper)

Models of $p$-adic mechanics

E. I. Zelenov


Abstract: We segregate the class of ultrametric ($p$-adic) systems within the standard models of classical and quantum mechanics. We show that ultrametric models can be described in the language of standard models but also have several distinguishing properties. In particular, we show that a stronger Poincaré recurrence theorem holds for classical ultrametric dynamical systems. As an example of a quantum $p$-adic system, we consider the algebra of commutation relations of the one-dimensional quantum mechanics. We show that this algebra, as in the real case, is isomorphic to the algebra of compact operators.

Keywords: ultrametric, $p$-adic classical mechanics, $p$-adic quantum mechanics

DOI: https://doi.org/10.4213/tmf8411

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English version:
Theoretical and Mathematical Physics, 2013, 174:2, 247–252

Bibliographic databases:

Document Type: Article
Received: 10.09.2012

Citation: E. I. Zelenov, “Models of $p$-adic mechanics”, TMF, 174:2 (2013), 285–291; Theoret. and Math. Phys., 174:2 (2013), 247–252

Citation in format AMSBIB
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\paper Models of $p$-adic mechanics
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\vol 174
\issue 2
\pages 285--291
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\elib{http://elibrary.ru/item.asp?id=20732580}
\transl
\jour Theoret. and Math. Phys.
\yr 2013
\vol 174
\issue 2
\pages 247--252
\crossref{https://doi.org/10.1007/s11232-013-0021-5}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874849581}


Linking options:
  • http://mi.mathnet.ru/eng/tmf8411
  • https://doi.org/10.4213/tmf8411
  • http://mi.mathnet.ru/eng/tmf/v174/i2/p285

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. I. Zelenov, “$p$-Adic model of quantum mechanics and quantum channels”, Proc. Steklov Inst. Math., 285 (2014), 132–144  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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