only below the light cone, retardation leads to an infinitely small contribution even above the light cone, giving a definite sign to the self-energies for all energies: ${\varepsilon}({\text{Im}}{\Pi_\text{T}}(\omega))=-{\varepsilon}(\omega)$, ${\varepsilon}({\text{Im}}{\Pi_\text{L}}(\omega))=+{\varepsilon}(\omega)$ and ${\varepsilon}({\text{Im}}\Sigma_{\pm}(\omega))=\mp1$. Note that this is not related to Landau damping which is found below the light cone only.

The HTL propagators follow from Dyson’s equations as ${D_\text{T}}^{-1}=-\omega^{2}+k^{2}+{\Pi_\text{T}}$, ${D_\text{L}}^{-1}=-k^{2}-{\Pi_\text{L}}$ and $S_{\pm}^{-1}=-\omega\pm(k+\Sigma_{\pm})$. On-shell (quasi)particles satisfy a dispersion relation determined by ${\text{Re}}D_{\text{T},\text{L}}^{-1}=0$ and ${\text{Re}}S_{\pm}^{-1}=0$ respectively. It is, therefore, useful to first investigate the real part of the inverse retarded HTL propagators.

![The real parts of the inverse gluon propagators $D_{\text{T,L}}^{-1}$ scaled by the Debye screening mass squared are shown as functions of the energy $\omega$ scaled by the momentum $k$ which is fixed at $k=0.5T$. \[fig:ReGluPropm1\]](ReDTm1xGraph2.eps "fig:")        ![The real parts of the inverse gluon propagators $D_{\text{T,L}}^{-1}$ scaled by the Debye screening mass squared are shown as functions of the energy $\omega$ scaled by the momentum $k$ which is fixed at $k=0.5T$. \[fig:ReGluPropm1\]](ReDLm1xGraph2.eps "fig:")

![The real parts of the inverse quark propagators $S_{\pm}^{-1}$ scaled by the fermionic mass parameter squared are shown as functions of the energy $\omega$ scaled by the momentum $k$ which is fixed at $k=0.5T$. \[fig:ReQuarkPropm1\]](ReSplusm1xGraph2.eps "fig:")        ![The real parts of 