Some properties of orbit space in Yang-Mills theory (Q789761)

Since the quark confinement phenomenon is connected with gauge invariance and compactness of the space considered in the corresponding theory, the author studies in the Yang-Mills theory the properties of its orbit space \({\mathcal O}\). The latter is a collection of classes of gauge invariant fields. It is shown that \({\mathcal O}\) contains infinite dimensional Euclidean subspaces, hence \({\mathcal O}\) is non-compact. It is also inferred that the Ricci tensor of \({\mathcal O}\) is positive definite, so that \({\mathcal O}\) tends to be closed.