Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2017, Volume 20, Issue 2, 1750008, 23 pp.
Stochastic Lévy differential operators and Yang–Mills equations
Boris ╬. Volkov
Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow 119991, Russiaof Russian Academy of Sciences, Moscow
The relationship between the Yang–Mills equations and the stochastic analogue of Lévy
differential operators is studied. The value of the stochastic Lévy–Laplacian is found by
means of Cèsaro averaging of directional derivatives on the stochastic parallel transport.
It is shown that the YangľMills equations and the Lévy–Laplace equation for such
Laplacian are not equivalent in contrast to the deterministic case. An equation equivalent
to the Yang–Mills equations is obtained. The equation contains the Lévy divergence.
It is proved that the Yang–Mills action functional can be represented as an infinitedimensional
analogue of the Direchlet functional of a chiral field. This analogue is also
derived using Cèsaro averaging.
|Russian Science Foundation
|This work is supported by the Russian Science Foundation Under Grant 14-50-00005.
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