Levy Laplacian on manifold and Yang-Mills heat flow
Mathematical Physics
2020-10-02 v3 math.MP
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.
Keywords
Cite
@article{arxiv.1905.01223,
title = {Levy Laplacian on manifold and Yang-Mills heat flow},
author = {Boris O. Volkov},
journal= {arXiv preprint arXiv:1905.01223},
year = {2020}
}
Comments
15 pages, minor changes