solution of ${\text{Re}}S_{-}^{-1}=0$. The remaining two dispersion relations represent collective quark excitations: the positive energy dispersion relation related to $S_{-}$ describes the plasminos, while the negative energy solution of ${\text{Re}}S_{+}^{-1}=0$ represents antiplasminos. Again, a tachyonic solution appears within the regime of Landau damping.

The evolution of the zeros of the real part of the inverse retarded propagators as a function of the momentum $k$ gives the dispersion relations $\omega_{i,k}$. These dispersion relations cannot be expressed as analytic functions $\omega(k)$ in closed form. ${\text{Re}}D_{i}^{-1}(\omega,\, k,\,\Pi_{i}(\omega,k))=0$ and ${\text{Re}}S_{i}^{-1}(\omega,\, k,\,\Sigma_{i}(\omega,k))=0$ lead to transcendental equations and have to be solved numerically. The results are shown in Figures \[fig:disp gluons\] and \[fig:disp quarks\]. Due to the above parity property quarks and antiquarks obey identical dispersion relations up to the sign, as do plasminos and antiplasminos.

![The dispersion relations $\omega_{\text{T},k}$ of transverse and $\omega_{\text{L},k}$ of longitudinal gluon modes scaled by the Debye screening mass are shown as functions of the momentum $k$ scaled by the Debye screening mass in linear (left) and quadratic (right) scales.\[fig:disp gluons\]](GluonsLinear2.eps "fig:")        ![The dispersion relations $\omega_{\text{T},k}$ of transverse and $\omega_{\text{L},k}$ of longitudinal gluon modes scaled by the Debye screening mass are shown as functions of the momentum $k$ scaled by the 