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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 151, Pages 21–36 (Mi into337)  
This article is cited in 1 scientific paper (total in 1 paper)

Applications of Lévy Differential Operators in the Theory of Gauge Fields

B. O. Volkovab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Bauman Moscow State Technical University
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Abstract: This paper is a survey of results on the relationship between gauge fields and infinite-dimensional equations for parallel transport that contain the Lévy Laplacian or the divergence associated with this Laplacian. Also we analyze the deterministic case where parallel transports are operator-valued functionals on the space of curves and the case of the Malliavin calculus where (stochastic) parallel transports are operator-valued Wiener functionals.
Keywords: Lévy Laplacian, Lévy divergence, gauge field, Yang–Mills equations, instanton, Malliavin calculus.
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 252, Issue 1, Pages 20–35
DOI: https://doi.org/10.1007/s10958-020-05138-9
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 60H40, 81T13
Language: Russian
Citation: B. O. Volkov, “Applications of Lévy Differential Operators in the Theory of Gauge Fields”, Quantum probability, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 151, VINITI, Moscow, 2018, 21–36; J. Math. Sci. (N. Y.), 252:1 (2021), 20–35
Citation in format AMSBIB
\Bibitem{Vol18}
\by B.~O.~Volkov
\paper Applications of L\'evy Differential Operators in the Theory of Gauge Fields
\inbook Quantum probability
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 151
\pages 21--36
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into337}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3903363}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 252
\issue 1
\pages 20--35
\crossref{https://doi.org/10.1007/s10958-020-05138-9}
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