Wormhole instanton solution in the Einstein-Yang-Mills system

A spherical symmetric classical solution of the Einstein and the SU(2) Yang-Mills equations is found in the four-dimensional euclidean space-time with cosmological constant. The isospinor fermion has zero modes. Their cosmological implications are also discussed with an emphasis on the fact that wormhole instantons in general can be found not only in the sub-Planck physics but also in almost all stages in lower energy physics. (orig.)