Exact Classical Solutions of the Coupled System of O(5) Gauge Fields with Massless Scalar Fields in Euclidean Space
Abstract
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 spacetime (i.e., conformal) symmetry indices as in the cases of the instanton or the meron solutions. This identification of the internal and spacetime indices takes the simplest form when the coupled equations are expressed on a fourdimensional Euclidean sphere S^{4}, 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 (5component) representation, turns out to be proportional to the radial vector of S^{4}. The whole system is regular everywhere on S^{4} and gives a finite Euclidean action. Comments on the analogous solutions of the coupled O(4,1) gauge fields with massless scalar fields in Minkowski space are given.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 July 1979
 DOI:
 10.1143/PTP.62.214
 Bibcode:
 1979PThPh..62..214S