Abstract:
It is shown that partial differential equations with almost periodic coefficients can be obtained by a quantization like Weyl quantization on R2n from Hamilton[an systems on the cotangent bundle of some infinite-dimensional manifold, the Bohr compactifieation. Hamilton[an and quantum mechanics are also constructed on the cotangent bundle of an arbitrary compact connected Abelian group.
Citation:
M. A. Antonets, I. A. Shereshevskii, “Weyl quantization on compact Abelian groups and the quantum mechanics of almost periodic systems”, TMF, 48:1 (1981), 49–59; Theoret. and Math. Phys., 48:1 (1981), 597–604
\Bibitem{AntShe81}
\by M.~A.~Antonets, I.~A.~Shereshevskii
\paper Weyl quantization on compact Abelian groups and the quantum mechanics of almost periodic systems
\jour TMF
\yr 1981
\vol 48
\issue 1
\pages 49--59
\mathnet{http://mi.mathnet.ru/tmf4471}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=630269}
\zmath{https://zbmath.org/?q=an:0471.43008}
\transl
\jour Theoret. and Math. Phys.
\yr 1981
\vol 48
\issue 1
\pages 597--604
\crossref{https://doi.org/10.1007/BF01037984}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981ND61200006}
Linking options:
https://www.mathnet.ru/eng/tmf4471
https://www.mathnet.ru/eng/tmf/v48/i1/p49
This publication is cited in the following 3 articles:
Yi Wu, Yonghui Xia, Shengfu Deng, “Existence and Stability of Pseudo Almost Periodic Solutions for a Delayed Multispecies Logarithmic Population Model with Feedback Control”, Qual. Theory Dyn. Syst., 20:1 (2021)
S. S. Akbarov, “Smooth structure and differential operators on a locally compact group”, Izv. Math., 59:1 (1995), 1–44
S. S. Akbarov, “Differential geometry and quantization on a locally compact group”, Izv. Math., 59:2 (1995), 271–286
Citation in format AMSBIB
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