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TMF, 1991, Volume 86, Number 2, Pages 177–190 (Mi tmf5433)  

This article is cited in 2 scientific papers (total in 2 papers)

Real non-Archimedean structure of spacetime

A. Yu. Khrennikov


Abstract: A study is made of the process of measurement by means of $m$-adic (and, in particular, $p$-adic) numbers. It is shown that $m$-adic variables can be interpreted as variables that are infinite!y large compared with the unit of measurement. Morita's F function is used to construct a Bargmann–Fock representation for a non-Archimedean harmonic oscillator with infinitely high energies. A gauge connection between the real geometry of Minkowski spacetime $M_4$ and non-Archimedean geometry of the microscopic world is considered. Groups of non-Archimedean symmetries are realized as internal symmetries. The concept of a real non-Archimedean manifold is introduced. A group of conformal transformations associated with a Galois group is constructed.

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English version:
Theoretical and Mathematical Physics, 1991, 86:2, 121–130

Bibliographic databases:

Received: 02.07.1990

Citation: A. Yu. Khrennikov, “Real non-Archimedean structure of spacetime”, TMF, 86:2 (1991), 177–190; Theoret. and Math. Phys., 86:2 (1991), 121–130

Citation in format AMSBIB
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\by A.~Yu.~Khrennikov
\paper Real non-Archimedean structure of spacetime
\jour TMF
\yr 1991
\vol 86
\issue 2
\pages 177--190
\mathnet{http://mi.mathnet.ru/tmf5433}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1107699}
\zmath{https://zbmath.org/?q=an:0753.46042}
\transl
\jour Theoret. and Math. Phys.
\yr 1991
\vol 86
\issue 2
\pages 121--130
\crossref{https://doi.org/10.1007/BF01016162}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GH61300002}


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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. A. Yu. Khrennikov, “Generalized functions on a Non-Archimedean superspace”, Math. USSR-Izv., 39:3 (1992), 1209–1238  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. S. V. Kozyrev, “Methods and Applications of Ultrametric and $p$-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84  mathnet  crossref  crossref  zmath  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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