I present a general approach to de Sitter and anti de Sitter Quantum Field Theory based on the global analyticity properties of the correlation functions which does not make use of particular coordinate system.
In this context I introduce an important family of plane waves well adapted to the de Sitter geometry and discuss the harmonic analysis of propagators in terms of them. Applications include the Kallen-Lehmann representations and 1-loop and two-loop calculations in the dimensional regularization in both the de Sitter and the anti de Sitter cases.
