Lattice Landau gauge gluon propagator at finite temperature: non-zero Matsubara frequencies and spectral densities

The lattice Landau gauge gluon propagator at finite temperature is computed including the non-zero Matsubara frequencies. Furthermore, the K"all'en-Lehmann representation is inverted and the corresponding spectral density evaluated using a Tikhonov regularisation together with the Morozov discrepancy principle. Implications for gluon confinement are discussed.