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.