Levy Laplacians and instantons on manifolds

Volkov Boris O.

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Levy Laplacians and instantons on manifolds

机译：歧管的Laplacians和instantons

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摘要

The equivalence of the anti-selfduality Yang-Mills equations on the four-dimensional orientable Riemannian manifold and the Laplace equations for some infinite-dimensional Laplacians is proved. A class of modified Levy Laplacians parameterized by the choice of a curve in the group SO(4) is introduced. It is shown that a connection is an instanton (a solution of the anti-selfduality Yang-Mills equations) if and only if the parallel transport generalized by this connection is a solution of the Laplace equations for some three modified Levy Laplacians from this class.

机译：证明了四维可定向黎曼歧管上的抗自身性杨铣刀等同物和一些无限维拉普利人的拉普拉斯方程。介绍了一类通过选择组中的曲线参数化的修改的征用拉普拉斯，如此（4）。结果表明，如果仅当通过该连接的并行传输是通过该课程的三个改进的征收拉普拉斯人的Laplace方程的解决方程，则连接是一个算法（反自身性yang-mills方程的解决方案）。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2020年第2期|共20页
作者
Volkov Boris O.;
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作者单位

Steklov Math Inst Ul Gubkina 8 Moscow 119991 Russia;

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原文格式 PDF
正文语种 eng
中图分类物理学;
关键词
Levy Laplacian; Yang-Mills equations; instantons; infinite-dimensional manifold;

机译：Levy Laplacian;阳轧机方程;instantons;无限的歧管;

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4. Levy Laplacians and instantons on manifolds [J] . Volkov Boris O. Infinite dimensional analysis, quantum probability, and related topics . 2020,第2期

机译：歧管的Laplacians和instantons
5. Levy Laplacian on Manifold and Yang—Mills Heat Flow [J] . Lobachevskii journal of mathematics . 2019,第10期

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Levy Laplacians and instantons on manifolds

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