in (64) describe  the  change  of  the  field
energy, field momentum and the effect of external forces.  They  depend
on the concrete type of interaction.
\par
    If there are no external fields then the last three terms in (64)
should be omitted and the energy and momentum fluxes are:
\begin{equation}
Q_i   =   E\dot{u}_i + \ang{\eps\frac{\partial H}{\partial
p_i}f}
 - \frac{1}{2}\dot{u}^2 J_i + \Pi_{ik} \dot{u}_k$$ $$\begin{aligned}
\Pi_{ik}  =
 - (\sigma_{ik} + E_0\delta_{ik})
 + \rho\dot{u}_i\dot{u}_k
%\nonumber \\
 +
 \langle\lambda_{ik}f\rangle
-m \left \langle f\frac{\partial \eps}{\partial p_i}\frac{\partial
\eps}{\partial p_k}\right  \rangle
 + m \left \langle f\frac{\partial H}{\partial p_i}\frac{\partial
H}{\partial p_k} \right \rangle .\end{aligned}$$

The momentum flux tensor consists of two parts, $L_{ik}$ and $P_{ik}$, which correspond to the contributions of the lattice and quasiparticles respectively: $$L_{ik} = -(\sigma_{ik} + E_0 \delta_{ik}) + \rho_0 {\dot u}_i {\dot u}_k
\ee          %68
\begin{equation}
P_{ik} = \langle \lambda^0_{ik} f\rangle +
m \left \langle f \frac{\p H}{\p p_i} \frac{\p H}{\p p_k}\right\rangle
\ee             %69
where
$$
 \langle \lambda^0_{ik} f\rangle =
 \langle \lambda_{ik} f\rangle
- m \left \langle f \frac{\p \eps}{\p p_i}
\frac{\p \eps}{\p p_k} \right \rangle
$$
is the quasiparticle momentum flux tensor in the system of centre of mass
while $ \langle \lambda_{ik} f\rangle $ corresponds to the co-moving frame.
It 