Geometrical gauge theory of ghost and Goldstone fields and of ghost symmetries

We provide a geometrical identification of the ghost fields, essential to the renormalization procedure in the non-Abelian (Yang-Mills) case. These are some of the local components of a connection on a principal bundle. They multiply the differentials of coordinates spanning directions orthogonal to those of a given section, whereas the Yang-Mills potential multiplies the coordinates in the section itself. In the case of a supergroup, the ghosts become commutative for the odd directions, and represent Nambu-Goldstone fields. We apply the results to chiral "flavor" SU(3)(L) x SU(3)(R) and to SU(2/1). The latter reproduces a highly constrained Weinberg-Salam model.