Many faces of the Landau gauge gluon propagator at zero and finite temperature: positivity violation, spectral density and mass scales

We address several aspects of gluon propagation at zero and finite temperature. In particular, we study the violation of spectral positivity, we discuss a method to extract the K"all'{e}n-Lehmann spectral density of a particle (be it elementary or bound state) propagator and apply it to compute gluon spectral densities from lattice data. Furthermore, we also consider the interpretation of the Landau gauge gluon propagator at finite temperature as a massive type bosonic propagator.