The spectral density for scalar �elds in de Sitter space at one-loop

We review the Källén-Lehmann spectral representation in �at spacetime before moving on to de Sitter space. We compute one-loop corrections of de Sitter invariant two-point functions in the Lorentzian signature which are de�ned by the interacting Euclidean vacuum for scalar �elds with cubic interactions. These apply to all massive scalars in the complementary and principal series. Our investigations are motivated by the behaviour of the spectral density at the one-loop level whereby we can �nd a general expression relating the two-point function and the free propagators. Using well established techniques for treating quantum �elds in de Sitter, we compute the spectral density for speci�c cases, in both complementary and principal series in three dimensions and discuss the nature of particle stability. We also comment on extending this beyond the one-loop level