Euclidean Yang-Mills flows in the orbit space

Abstract

We establish a global setting for the canonical formalism of the Euclidean Yang-Mills theory in the orbit space M. In this setting it is shown that the Euclidean Yang-Mills equations lead to an ordinary second order differential system of M and the (anti) self-dual solutions are in the flow of a densely defined vector field ±H of M. We also prove that, for the particular case of having T³ as space manifold the flows ±H are homotopic complete, i.e., in each class of π₁(M) there exists a closed integral curve of ±H.