  It is well known that in de Sitter space the (free) minimally coupled
massless scalar field theory does not admit any de Sitter-invariant Hadamard
state. Related to this is the fact that the propagator for the massive scalar
field corresponding to the de Sitter-invariant vacuum state diverges in the
massless limit, with the infrared-divergent term being a constant. Since the
Faddeev-Popov ghosts for the covariantly quantized Yang-Mills theory are
minimally coupled massless scalar fields, it might appear that de Sitter
symmetry would be broken in the ghost sector of Yang-Mills theory in de Sitter
space. It is shown in this paper that the modes responsible for de Sitter
symmetry breaking can be removed in a way consistent with BRST invariance and
that a de Sitter-invariant theory can be constructed. More generally, it is
shown that the spatially constant modes (the zero modes) of the Faddeev-Popov
ghosts can be disposed of in a wide class of spacetimes with compact spatial
sections. Then, the effective theory obtained by removing the zero modes, which
contains a non-local interaction term, is shown to be equivalent to the theory
corresponding to using a Faddeev-Popov-ghost propagator with the constant
infrared-divergent term removed, provided that one can freely integrate by
parts in the spacetime integral at the vertex for the ghost interaction term.
