Particles and fields on the de Sitter universe

In this paper we will give a short introduction to the geometry of the de Sitter universe and describe an approach to de Sitter Quantum Field Theory based on the complexification of the de Sitter manifold. We will also present some recent results about the stability of de Sitterian "particles" that have been obtained in a continuing collaboration with Jacques Bros and Henri Epstein. We will show that for particles with masses above a critical mass there is no such thing as particle stability, so that decays forbidden in flat space-time do occur in the de Sitter universe. The lifetime of one such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with lower mass are even stranger. The masses of their decay products must obey quantification rules, and their lifetime is zero. These results have been obtained at the first order of perturbative expansion of an interacting quantum field theory.