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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 151, Pages 21–36 (Mi into337)  

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

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

Full text: PDF file (268 kB)

Bibliographic databases:

UDC: 517.98
MSC: 60H40, 81T13

Citation: B. O. Volkov, “Applications of Lévy Differential Operators in the Theory of Gauge Fields”, Quantum probability, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 151, VINITI, Moscow, 2018, 21–36

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. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 151
\pages 21--36
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into337}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3903363}


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