Levy Laplacian on manifold and Yang-Mills heat flow

Abstract

A covariant definition of the Levy Laplacian on an infinite dimensional manifold is introduced. It is shown that a time-depended connection in a finite dimensional vector bundle is a solution of the Yang-Mills heat equations if and only if the associated flow of the parallel transports is a solution of the heat equation for the covariant Levy Laplacian on the infinite dimensional manifold.

arXiv comment15 pages, minor changes

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• Quasi-Feynman formulas -- a method of obtaining the evolution operator for the Schroedinger equation
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Cited by in corpus (2)

• Levy Laplacians and instantons on manifolds
• Modified Lévy Laplacian on manifold and Yang-Mills instantons