2013/01/31 by Masafumi Fukuma, Yuho Sakatani, Sotaro Sugishita · 30 citations
Mathematics · Physics and Astronomy · #Anti-de Sitter space #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #De Sitter space #De Sitter universe #Geometry #Light cone #Mathematical physics #Mathematics #Path integral formulation #Physics #Propagator #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Scalar (mathematics) #Scalar field #Spacetime #Universe #Vacuum state #gr-qc #hep-th
paper · pdf · open access · doi:10.1103/physrevd.88.024041
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 88(2) (American Physical Society) · 38 pages, 14 figures, v2: references added, discussion on the in-in propagators improved, v3: typos corrected, v4: references added, discussions improved, to appear in PRD
arxiv created 2013/07/08 · openalex publication_date 2013/07/23 · arxiv updated 2013/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In a spacetime with no global timelike Killing vector, we do not have a natural choice for the vacuum state of matter fields, which leads to an ambiguity in defining the Feynman propagators. In this paper, taking the vacuum state to be the instantaneous ground state of the Hamiltonian at each moment, we develop a method for calculating wave functions associated with the vacuum and the corresponding in-in and in-out propagators. We apply this method to free scalar field theory in de Sitter space and obtain de Sitter invariant propagators in various coordinate patches. We show that the in-out propagator in the Poincar'e patch has a finite massless limit in a de Sitter invariant form. We argue and numerically check that our in-out propagators agree with those obtained by a path integral with the standard i\ensuremathε prescription, and we identify the condition on a foliation of spacetime under which such coincidence can happen for the foliation. We also show that the in-out propagators satisfy Polyakov's composition law. Several applications of our framework are also discussed.