Gauge fields in mechanisms of spontaneous compactification of subspaces

It is shown that in the Cremmer–Scherk mechanism in spontaneous compaetifieation into the homogeneous spaces $G/H$ not all the gauge fields participate effectively but only the gauge fields of the subgroup $H$. The additional components of the gauge fields of the group $G$ can be eliminated by a gauge transformation that belongs to the group $G$. After the elimination of these additional gauge fields the Cremmer–Scherk mechanism of spontaneous eompactification reduces to the mechanism determined by associating the gauge fields with the $H$ connections on the spaces $G/H$.