The Hadamard function and the Feynman propagator in the AdS/CFT correspondence

We construct the retarded Green function and the Hadamard function in the Lorentzian (d+1)-dimensional anti-de Sitter spacetime for the Poincaré coordinate by performing the mode integration directly. We explore the structure of singularities for the position-space Feynman propagator derived from them. The boundary scaling limits of the bulk Feynman propagator yield the bulk-boundary propagator and the boundary conformal correlation function with an extra factor.