2016/10/31 by Claudio Dappiaggi, Hugo R. C. Ferreira · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Anti-de Sitter space #Black Holes and Theoretical Physics #Boundary (topology) #Boundary conformal field theory #Boundary value problem #Conformal map #Cosmology and Gravitation Theories #Geometry #Gravitational singularity #Hadamard transform #Mathematical analysis #Mathematical physics #Mathematics #Neumann boundary condition #Physics #Pure mathematics #Quantum mechanics #Robin boundary condition #Scalar (mathematics) #Scalar field #Spacetime #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.94.125016
published as Phys. Rev. D 94, 125016 (2016) · 30 pages, 2 figures. Publication version
arxiv created 2016/12/16 · openalex publication_date 2016/12/21 · arxiv updated 2016/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider a real, massive scalar field on PAdSd+1, the Poincar'e domain of the (d+1)-dimensional anti--de Sitter (AdS) spacetime. We first determine all admissible boundary conditions that can be applied on the conformal boundary, noting that there exist instances where ``bound states'' solutions are present. Then, we address the problem of constructing the two-point function for the ground state satisfying those boundary conditions, finding ultimately an explicit closed form. In addition, we investigate the singularities of the resulting two-point functions, showing that they are consistent with the requirement of being of Hadamard form in every globally hyperbolic subregion of PAdSd+1 and proposing a new definition of Hadamard states which applies to PAdSd+1.