Geodesic
L\'evy Laplacians and instantons
Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 226-238.

Voir la notice de l'article provenant de la source Math-Net.Ru

We describe dual and antidual solutions of the Yang–Mills equations by means of Lévy Laplacians. To this end, we introduce a class of Lévy Laplacians parameterized by the choice of a curve in the group $\mathrm {SO}(4)$. Two approaches are used to define such Laplacians: (i) the Lévy Laplacian can be defined as an integral functional defined by a curve in $\mathrm {SO}(4)$ and a special form of the second-order derivative, or (ii) the Lévy Laplacian can be defined as the Cesàro mean of second-order derivatives along vectors from the orthonormal basis constructed by such a curve. We prove that under some conditions imposed on the curve generating the Lévy Laplacian, a connection in the trivial vector bundle with base $\mathbb R^4$ is an instanton (or an anti-instanton) if and only if the parallel transport generated by the connection is harmonic for such a Lévy Laplacian. 
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     title = {L\'evy {Laplacians} and instantons},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a18/}
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B. O. Volkov. L\'evy Laplacians and instantons. Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 226-238. http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a18/

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