# Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions

October 04, 2016

We consider a real, massive scalar field on ${\rm PAdS}_{d+1}$, the
Poincar\'e domain of the $(d+1)$-dimensional 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
${\rm PAdS}_{d+1}$ and proposing a new definition of Hadamard states which
applies to ${\rm PAdS}_{d+1}$.

Keywords:

Hadamard states, boundary conditions, AdS spacetime