Exact Classical Solutions of the Coupled System of O(5) Gauge Fields with Massless Scalar Fields in Euclidean Space
Exact classical solutions of the coupled equations of O(5) gauge fields nad massless scalar fields in Euclidean space presented. The solutions are found by identifying the internal symmetry indices with the space-time (i.e., conformal) symmetry indices as in the cases of the instanton or the meron solutions. This identification of the internal and space-time indices takes the simplest form when the coupled equations are expressed on a four-dimensional Euclidean sphere S4, which is conformal to the Euclidean space having the group O(5) as the group of motions.The obtained gauge field solutions have the same form as the O(5) generalization of the instanton solution by Jackiw and Rebbi but with a different coefficient. The scalar field, chosen as a vector (5-component) representation, turns out to be proportional to the radial vector of S4. The whole system is regular everywhere on S4 and gives a finite Euclidean action. Comments on the analogous solutions of the coupled O(4,1) gauge fields with mass-less scalar fields in Minkowski space are given.