Unified spatial and isotopic symmetry in Yang–Mills fields

Continuous automorphisms of gauge fields are considered, which include the transformations of coordinates as well as gauge transformations. Equations for the generators of the group and the conditions of the invariance of the gauge field with respect to the unified symmetry group are derived. The formalism developed is applied to the description of the Yang–Mills fields with the symmetry $O(3)\times O(2)$ and the gauge group $SU(3)$.