Quantum fields in the static de Sitter universe

We construct explicit mode expansions of various tree-level propagators in the Rindler-de Sitter universe, also known as the static (or compact) patch of the de Sitter spacetime. We construct in particular the Wightman functions for thermal states having a generic temperature T. We give a fresh simple proof that the only thermal Wightman propagator that respects the de Sitter isometry is the restriction to the Rindler-de Sitter wedge of the propagator for the Bunch-Davies state. It is the thermal state with T=(2π)-1 in the units of de Sitter curvature. We show that propagators with T≠(2π)-1 are only time translation invariant and have extra singularities on the boundary of the static patch. We also construct the expansions for the so-called alpha-vacua in the static patch and discuss the flat limit