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 $k=0.5T$. \[fig:ReQuarkPropm1\]](ReSminusm1xGraph2.eps "fig:")

Due to symmetry properties of $D_{\text{T,L}}^{-1}$ there is just one positive-energy dispersion relation above the light cone: $\omega_{\text{T},k}$ and $\omega_{\text{L},k}$, respectively. This means that - up to the sign - transverse and longitudinal gluons have the same dispersion relations as their anti(quasi)particle counterparts. The additional tachyonic dispersion relation for longitudinal gluons is related to Landau damping. Figure \[fig:ReGluPropm1\] explicitly shows the real parts for fixed momentum $k=0.5T$. Both $D_{\text{T},\text{L}}^{-1}$ are symmetric with respect to $\omega$. The zero of ${\text{Re}}{D_\text{T}}^{-1}$ determines the dispersion relation $\omega_{\text{T},k}$ for transverse gluons. The zero of ${\text{Re}}{D_\text{L}}^{-1}$ above the light cone indicates the dispersion relation $\omega_{\text{L},k}$ of longitudinal gluons, while the tachyonic dispersion relation $\omega_{\text{L},k}^{t}$ (below the light cone) is due to Landau damping.

The inverse quark propagators are not symmetric but, as a consequence of the symmetry of the self-energy, satisfy the parity property ${\text{Re}}S_{+}^{-1}(-\omega)=-{\text{Re}}S_{-}^{-1}(\omega)$ (cf. Figure \[fig:ReQuarkPropm1\]). Hence, quarks are described by the positive energy dispersion relation related to $S_{+}$, while the dispersion relation of antiquarks is found from the negative energy 