Energy and momentum density of thermal gluon oscillations

In the exact propagator for finite temperature gluons the location of the transverse and longitudinal poles in the gluon propagator are unknown functions of wave vector: $\omega_{T}(k)$ and $\omega_{L}(k)$. The residues of the poles, also unknown, fix the normalization of the one gluon vector potential and thus of the field strength. The naive energy density $\pol{E}\cdot\pol{D}+\pol{B}\cdot\pol{H}$ is not correct because of dispersion. By keeping the modulations due to the source currents the energy density is shown to be $\omega_{T}/V$ and $\omega_{L}/V$ regardless of the functional form of $\omega_{T}(k)$ and $\omega_{L}(k)$. The momentum density is $k/V$. The resulting energy-momentum tensor is not symmetric.