Spherically symmetric solutions of Euclidean Yang-Mills equations

The authors consider the Euclidean Yang-Mills equations with symmetry group SU (2) and describe a transformation under which the action functional and the topological charge are invariant. The use of SU (2) symmetry permits them to apply Coleman's principle. A spherically symmetric ansatz is obtained by which the Yang-Mills and duality equations reduce to ordinary differential equations for a given function. It is shown that every solution provided by the ansatz for the Yang-Mills equations with finite action and positive (negative) charge satisfies the duality equations. The authors also describe explicitly all solutions of the ansatz form of the duality equations. Among them are the 1-instanton solutions of Belavin and polyakov