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TMF, 1990, Volume 83, Number 3, Pages 406–418 (Mi tmf5819)  

This article is cited in 5 scientific papers (total in 5 papers)

Quantum mechanics over non-Archimedean number fields

A. Yu. Khrennikov


Abstract: Schrödinger and Bargmann–Fock representations in non-Archimedean quantum mechanics are realized in the spaces $L_2(K^n,dx)$ and $L_2(Z^n,e^{-zz} dz d\bar z)$ ($K$ is a non-Archimedean field, and $Z=K(\sqrt\tau )$ is its quadratic extension) by means of the calculus of pseudodifferential operators.

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English version:
Theoretical and Mathematical Physics, 1990, 83:3, 623–632

Bibliographic databases:

Received: 17.10.1989

Citation: A. Yu. Khrennikov, “Quantum mechanics over non-Archimedean number fields”, TMF, 83:3 (1990), 406–418; Theoret. and Math. Phys., 83:3 (1990), 623–632

Citation in format AMSBIB
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\by A.~Yu.~Khrennikov
\paper Quantum mechanics over non-Archimedean number fields
\jour TMF
\yr 1990
\vol 83
\issue 3
\pages 406--418
\mathnet{http://mi.mathnet.ru/tmf5819}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1070695}
\zmath{https://zbmath.org/?q=an:0767.46044|0715.46050}
\transl
\jour Theoret. and Math. Phys.
\yr 1990
\vol 83
\issue 3
\pages 623--632
\crossref{https://doi.org/10.1007/BF01018032}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990EX50100009}


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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, “Mathematical methods of non-Archimedean physics”, Russian Math. Surveys, 45:4 (1990), 87–125  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. Yu. Khrennikov, “Generalized functions on a Non-Archimedean superspace”, Math. USSR-Izv., 39:3 (1992), 1209–1238  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. Yu. Khrennikov, “Real non-Archimedean structure of spacetime”, Theoret. and Math. Phys., 86:2 (1991), 121–130  mathnet  crossref  mathscinet  zmath  isi
    4. A. Yu. Khrennikov, “$p$-Adic probability theory and its applications. The principle of statistical stabilization of frequencies”, Theoret. and Math. Phys., 97:3 (1993), 1340–1348  mathnet  crossref  mathscinet  zmath  isi
    5. 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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