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

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Teoreticheskaya i Matematicheskaya Fizika, 1990, Volume 83, Number 3, Pages 406–418 (Mi tmf5819)

This article is cited in 8 scientific papers (total in 8 papers)

Quantum mechanics over non-Archimedean number fields

A. Yu. Khrennikov

Full-text PDF (1350 kB) Citations (8)

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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.

Received: 17.10.1989

English version:
Theoretical and Mathematical Physics, 1990, Volume 83, Issue 3, Pages 623–632
DOI: https://doi.org/10.1007/BF01018032

Bibliographic databases:

Language: Russian

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

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\yr 1990

\vol 83

\issue 3

\pages 406--418

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\mathscinet{http://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1990EX50100009}

Linking options:

https://www.mathnet.ru/eng/tmf5819

https://www.mathnet.ru/eng/tmf/v83/i3/p406

This publication is cited in the following 8 articles:

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
Anatoly N Kochubei, “p-adic commutation relations”, J. Phys. A: Math. Gen., 29:19 (1996), 6375
Andrew Khrennikov, “p-adic probability interpretation of Bell's inequality”, Physics Letters A, 200:3-4 (1995), 219
Andrew Khrennikov, “p-adic probability distributions of hidden variables”, Physica A: Statistical Mechanics and its Applications, 215:4 (1995), 577
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
A. Yu. Khrennikov, “Generalized functions on a Non-Archimedean superspace”, Math. USSR-Izv., 39:3 (1992), 1209–1238
A. Yu. Khrennikov, “Real non-Archimedean structure of spacetime”, Theoret. and Math. Phys., 86:2 (1991), 121–130
A. Yu. Khrennikov, “Mathematical methods of non-Archimedean physics”, Russian Math. Surveys, 45:4 (1990), 87–125

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

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Abstract page:	499
Full-text PDF :	220
References:	80
First page:	1

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