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

Removing the Faddeev-Popov zero modes from Yang-Mills theory in spacetimes with compact spatial sections