Applications of L\'evy Differential Operators in the Theory of Gauge Fields

B. O. Volkov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum probability, Tome 151 (2018), pp. 21-36.

Résumé

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.

Détail

Keywords: Lévy Laplacian, gauge field, Yang–Mills equations, instanton
Mots-clés : Lévy divergence, Malliavin calculus.

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