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Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2017, Volume 20, Issue 2, 1750008, 23 pp. (Mi idaqp2)  

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

Abstract: 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.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation Under Grant 14-50-00005.


DOI: https://doi.org/10.1142/S0219025717500084


Bibliographic databases:

ArXiv: 1605.06024
Received: 13.05.2016
Accepted:28.09.2016
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