 The Faddeev–Popov ghost field "c" is unique among the new fields of our gauge-fixed theory in having a geometrical meaning beyond the formal requirements of the BRST procedure.It is a version of the Maurer–Cartan form on formula_50, which relates each right-invariant vertical vector field formula_51 to its representation (up to a phase) as a formula_8-valued field.This field must enter into the formulas for infinitesimal gauge transformations on objects (such as fermions ψ, gauge bosons "A"μ, and the ghost "c" itself) which carry a non-trivial representation of the gauge group.