Claudio Dappiaggi
We consider a real, massive scalar field on the Poincaré domain of the (d+1)-dimensional AdS spacetime. Since the background is not globally hyperbolic, first we determine all admissible boundary conditions that can be applied on the conformal boundary and, subsequently, we address the problem of constructing the advanced and retarded Green operators as well as the two-point function for the ground state satisfying those boundary conditions. We unveil that, in some cases, bound states exist, while, when they are absent, the two-point function can be explicitly written in terms of special functions. In addition, we investigate the singularities of the resulting state, showing that they are consistent with the requirement of being of Hadamard form in every globally hyperbolic subregion of the Poincaré patch.
