Modified L\'evy Laplacian on manifold and Yang-Mills instantons

TL;DR

This paper introduces a modified infinite-dimensional Laplacian on manifolds, parameterized by curves in the orthogonal group, and explores its connection to Yang-Mills instantons in four dimensions.

Contribution

It defines a new class of Laplacians on manifolds and establishes their relation to Yang-Mills instantons, advancing understanding of gauge theory solutions.

Findings

The Laplacian is related to instantons under specific conditions.

The operator is constructed as a Cesàro mean of second order derivatives.

Connections between geometric operators and gauge theory are demonstrated.

Abstract

An infinite dimensional Laplacian defined as the Ces\'aro mean of the second order directional derivatives on manifold is considered. This Laplacian is parameterized by the choice of a curve in the group of orthogonal rotations. It is shown that, under certain conditions on the curve, this operator is related to instantons on a 4-dimensional manifold.