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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2004, Volume 245, Pages 72–85
(Mi tm173)
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This article is cited in 11 scientific papers (total in 11 papers)
$p$-Adic and Adelic Quantum Mechanics
B. G. Dragovich University of Belgrade
Abstract:
$p$-Adic mathematical physics emerged as a result of efforts to find a non-Archimedean approach to the space–time and string dynamics at the Planck scale. One of its main achievements is a successful formulation and development of $p$-adic and adelic quantum mechanics, which have complex-valued wave functions of $p$-adic and adelic arguments, respectively. Various aspects of these quantum mechanics are reviewed here. In particular, the corresponding Feynman's path integrals, some minisuperspace cosmological models, and relevant approaches to string theory are presented. As a result of an adelic approach, $p$-adic effects exhibit a space–time and some other discreteness, which depend on the adelic quantum state of the physical system under consideration. In addition to the review, this article also contains some new results.
Received in October 2003
Citation:
B. G. Dragovich, “$p$-Adic and Adelic Quantum Mechanics”, Selected topics of $p$-adic mathematical physics and analysis, Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov, Trudy Mat. Inst. Steklova, 245, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 72–85; Proc. Steklov Inst. Math., 245 (2004), 64–77
Linking options:
https://www.mathnet.ru/eng/tm173 https://www.mathnet.ru/eng/tm/v245/p72
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