‘removing the Faddeev-popov Zero Modes from Yang-mills Theory in Spacetimes with Compact Spatial Sections’ Author(s):

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 prop-agator 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.