Geodesic
Applications of L\'evy Differential Operators in the Theory of Gauge Fields
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum probability, Tome 151 (2018), pp. 21-36

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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, gauge field, Yang–Mills equations, instanton
Mots-clés : Lévy divergence, Malliavin calculus. 
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     author = {B. O. Volkov},
     title = {Applications of {L\'evy} {Differential} {Operators} in the {Theory} of {Gauge} {Fields}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
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B. O. Volkov. Applications of L\'evy Differential Operators in the Theory of Gauge Fields. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum probability, Tome 151 (2018), pp. 21-36. http://geodesic.mathdoc.fr/item/INTO_2018_151_a2/