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Keldysh Institute preprints, 2015, 057, 23 pages (Mi ipmp2019)  

This article is cited in 4 scientific papers (total in 4 papers)

Feynman formulas for averaging of semigroups, generating by the operators of Schrödinger type

L. A. Borisov, Yu. N. Orlov, V. Zh. Sakbaev


Abstract: The averaging procedure of one-parametric semigroups, based on Chernoff equivalence for operator-functions is constructed. The initial problem solutions are investigated for fractional diffusion equation and for Schrödinger equation with relativistic Hamiltonian of freedom motion. It is established, that in these examples the quantization can be treated as averaging of random translation operators in classical coordinate space.

Keywords: one-parametric semigroup, random variable, Hamiltonian, Chernoff theorem, Feynman formula, Chernoff equivalence.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00145
Russian Science Foundation 14-11-00687


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Document Type: Preprint

Citation: L. A. Borisov, Yu. N. Orlov, V. Zh. Sakbaev, “Feynman formulas for averaging of semigroups, generating by the operators of Schrödinger type”, Keldysh Institute preprints, 2015, 057, 23 pp.

Citation in format AMSBIB
\Bibitem{BorOrlSak15}
\by L.~A.~Borisov, Yu.~N.~Orlov, V.~Zh.~Sakbaev
\paper Feynman formulas for averaging of semigroups, generating by the operators of Schr\"odinger type
\jour Keldysh Institute preprints
\yr 2015
\papernumber 057
\totalpages 23
\mathnet{http://mi.mathnet.ru/ipmp2019}


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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. L. A. Borisov, Yu. N. Orlov, V. Zh. Sakbaev, “Ekvivalentnost po Chernovu primenitelno k uravneniyam evolyutsii matritsy plotnosti i funktsii Vignera dlya lineinogo kvantovaniya”, Preprinty IPM im. M. V. Keldysha, 2015, 066, 28 pp.  mathnet
    2. Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Unbounded random operators and Feynman formulae”, Izv. Math., 80:6 (2016), 1131–1158  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. Zh. Sakbaev, “Averaging of random walks and shift-invariant measures on a Hilbert space”, Theoret. and Math. Phys., 191:3 (2017), 886–909  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. Yu. N. Orlov, “O kommutatsii kvantovykh operatorov pervykh integralov gamiltonovykh sistem”, Preprinty IPM im. M. V. Keldysha, 2018, 018, 15 pp.  mathnet  crossref
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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