2014/10/31 by Jos Gibbons, Atsushi Higuchi · 9 citations
Physics and Astronomy · #Anti-de Sitter space #Black Holes and Theoretical Physics #Cosmological constant #Cosmology and Gravitation Theories #De Sitter space #De Sitter universe #Massless particle #Mathematical physics #Physics #Propagator #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Scalar field #Universe #de Sitter invariant special relativity #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.91.024006
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 91(2) (American Physical Society) · 17 pages, 1 figure
openalex publication_date 2015/01/06 · arxiv created 2015/01/07 · arxiv updated 2015/05/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 nonlocal 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.